Problem library

Find a problem

Search by course or topic.

Search problems

Area

AllMathPhysics

SubjectCourseTopic

Topic choices for Multivariable and Vector Calculus are shortened. Search still covers every problem.

More filters

StatusSkillProblem styleFind a private labelPrivate labelFavorites

Clear

Browsing still works.Sign in to add progress, saved problems and private labels.

Progress labels

IndependentSolved with helpIncorrect / unresolvedDraft in progressNot attemptedReview due

Problem results

ProblemsBuild a practice set

MVC:010117Resolve two tangent branches at a singular intersection

View access options

Mvc Surface Intersection TangentsMvc Regular Level Set Rank

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010118Locate the shortest connector between two skew lines

View access options

Mvc Skew Line DistanceMvc Quadratic Optimization

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010217Differentiate normalization as a tangent projection

View access options

Mvc Vector Valued DerivativesMvc Linearization Tangent Spaces

PrivateLabels unavailable

Private saving unavailable

Multivariable limits, continuity, and differentiationMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010218Differentiate an implicit surface through a mixed partial

View access options

Mvc Implicit Function PartialsMvc Mixed Partial Chain Rule

PrivateLabels unavailable

Private saving unavailable

Multivariable limits, continuity, and differentiationMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010219Transfer a physical direction through a nonlinear coordinate map

View access options

Mvc Matrix Chain RuleMvc Coordinate Velocity Transfer

PrivateLabels unavailable

Private saving unavailable

Multivariable limits, continuity, and differentiationMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010220Expose what a singular coordinate pullback hides at the origin

View access options

Mvc Inverse Chain RuleMvc Differentiability Counterexamples

PrivateLabels unavailable

Private saving unavailable

Multivariable limits, continuity, and differentiationMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010317Find the largest axis-aligned box inside an ellipsoid

View access options

Mvc Lagrange MultipliersMvc Global Constrained Extrema

PrivateLabels unavailable

Private saving unavailable

Constrained optimization and Lagrange multipliersMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010318Diagnose a constrained minimum missed by multiplier equations

View access options

Mvc Singular ConstraintsMvc Lagrange Hypothesis Audit

PrivateLabels unavailable

Private saving unavailable

Constrained optimization and Lagrange multipliersMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010417Straighten a product-ratio region with logarithms

View access options

Mvc Change OF VariablesMvc Jacobian Log Coordinates

PrivateLabels unavailable

Private saving unavailable

Multiple integration and change of variablesMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010418Find the centroid height of a sphere-cone intersection

View access options

Mvc Spherical Triple IntegralsMvc Centroid First Moments

PrivateLabels unavailable

Private saving unavailable

Multiple integration and change of variablesMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010419Square an annular sector to evaluate a singular-looking integral

View access options

Mvc Change OF VariablesMvc Nonlinear Map Injectivity

PrivateLabels unavailable

Private saving unavailable

Multiple integration and change of variablesMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010420Repair a doubled integral caused by a two-to-one coordinate map

View access options

Mvc Change OF Variables MultiplicityMvc Map Hypothesis Audit

PrivateLabels unavailable

Private saving unavailable

Multiple integration and change of variablesMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010517Compute an ellipse circulation two independent ways

View access options

Mvc Planar Line IntegralsMvc Greens Theorem

PrivateLabels unavailable

Private saving unavailable

Vector fields, line integrals, and Green's theoremMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010518Check outward flux across a parabolic cap

View access options

Mvc Green Flux FormMvc Curved Boundary Orientation

PrivateLabels unavailable

Private saving unavailable

Vector fields, line integrals, and Green's theoremMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010617Orient a triangular Stokes calculation

View access options

Mvc Stokes TheoremMvc Surface Boundary Orientation

PrivateLabels unavailable

Private saving unavailable

Surface integrals, divergence theorem, and Stokes' theoremMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010618Balance flux across a capped paraboloid

View access options

Mvc Divergence TheoremMvc Oriented Flux Graphs

PrivateLabels unavailable

Private saving unavailable

Surface integrals, divergence theorem, and Stokes' theoremMultivariable and Vector Calculus · Mixed review

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917011Let \mathbf v=\langle 6,-2,3\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917012A particle is acted on by the constant force \mathbf F=\langle 4,-2,5\rangle, measured in newtons.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917013Let \mathbf u=\langle 2,-1,3\rangle and \mathbf v=\langle 1,4,-2\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917014Let \mathbf u=\langle 1,2,2\rangle and \mathbf v=\langle 2,1,-2\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917015Let A=(1,1,1), B=(2,3,4), and C=(0,2,3).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917016Let \mathbf u=\langle 2,0,1\rangle, \mathbf v=\langle 1,3,0\rangle, and \mathbf w=\langle 0,1,4\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917017The diagonals of a parallelogram in \mathbb R^3 are the vectors \mathbf d_1=\langle 3,1,2\rangle and \mathbf d_2=\l…

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917018A line L passes through the points A=(3,-1,2) and B=(5,3,1).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917019For each pair of lines below, determine whether the lines are identical, distinct and parallel, intersecting but no…

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917020Let P=(1,2,3), and let L be the line through A=(0,1,1) and B=(2,3,0).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917021Let P=(1,0,-1), Q=(2,1,3), and R=(3,-1,1).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917022Consider the planes (a) For each of \Pi_2, \Pi_3, and \Pi_4, determine whether the plane is parallel to \Pi_1, perp…

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917023Let L be the line given by \mathbf r(t)=\langle 1,0,2\rangle+t\langle 2,-1,2\rangle, and let \Pi be the plane x+2y-…

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917024Let P=(3,-1,2) and let \Pi be the plane 2x-2y+z=5.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917025Consider the planes x-2y+2z=4 and -2x+4y-4z=6.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917026Let L_1 be the line x=1+t, y=t, z=2-t, and let L_2 be the line x=2s, y=1-s, z=s.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917027Let \Pi_1 be the plane x+y-z=2 and let \Pi_2 be the plane 2x-y+z=1.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917028Let L be the line given in symmetric form by and let P=(1,1,1).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917029By completing the square, rewrite in standard form.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917030Identify each of the following surfaces.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917031Let for all real t at which the expression is defined as a vector in \mathbb{R}^{3} with t\neq 2.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917032Let C be the curve of intersection of the circular cylinder x^{2}+y^{2}=16 and the plane z=x-2y+3.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917033Let C be the intersection of the sphere x^{2}+y^{2}+z^{2}=9 and the plane z=1.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917034Let \mathbf{r}(t)=\langle t^{2}-t,\ e^{2t},\ \cos t\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Problem library

Find a problem

Search by course or topic.

Search problems

Area

AllMathPhysics

SubjectCourseTopic

Topic choices for Multivariable and Vector Calculus are shortened. Search still covers every problem.

More filters

StatusSkillProblem styleFind a private labelPrivate labelFavorites

Clear

Browsing still works.Sign in to add progress, saved problems and private labels.

Progress labels

IndependentSolved with helpIncorrect / unresolvedDraft in progressNot attemptedReview due

Problem results

ProblemsBuild a practice set

MVC:010117Resolve two tangent branches at a singular intersection

View access options

Mvc Surface Intersection TangentsMvc Regular Level Set Rank

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010118Locate the shortest connector between two skew lines

View access options

Mvc Skew Line DistanceMvc Quadratic Optimization

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010217Differentiate normalization as a tangent projection

View access options

Mvc Vector Valued DerivativesMvc Linearization Tangent Spaces

PrivateLabels unavailable

Private saving unavailable

Multivariable limits, continuity, and differentiationMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010218Differentiate an implicit surface through a mixed partial

View access options

Mvc Implicit Function PartialsMvc Mixed Partial Chain Rule

PrivateLabels unavailable

Private saving unavailable

Multivariable limits, continuity, and differentiationMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010219Transfer a physical direction through a nonlinear coordinate map

View access options

Mvc Matrix Chain RuleMvc Coordinate Velocity Transfer

PrivateLabels unavailable

Private saving unavailable

Multivariable limits, continuity, and differentiationMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010220Expose what a singular coordinate pullback hides at the origin

View access options

Mvc Inverse Chain RuleMvc Differentiability Counterexamples

PrivateLabels unavailable

Private saving unavailable

Multivariable limits, continuity, and differentiationMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010317Find the largest axis-aligned box inside an ellipsoid

View access options

Mvc Lagrange MultipliersMvc Global Constrained Extrema

PrivateLabels unavailable

Private saving unavailable

Constrained optimization and Lagrange multipliersMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010318Diagnose a constrained minimum missed by multiplier equations

View access options

Mvc Singular ConstraintsMvc Lagrange Hypothesis Audit

PrivateLabels unavailable

Private saving unavailable

Constrained optimization and Lagrange multipliersMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010417Straighten a product-ratio region with logarithms

View access options

Mvc Change OF VariablesMvc Jacobian Log Coordinates

PrivateLabels unavailable

Private saving unavailable

Multiple integration and change of variablesMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010418Find the centroid height of a sphere-cone intersection

View access options

Mvc Spherical Triple IntegralsMvc Centroid First Moments

PrivateLabels unavailable

Private saving unavailable

Multiple integration and change of variablesMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010419Square an annular sector to evaluate a singular-looking integral

View access options

Mvc Change OF VariablesMvc Nonlinear Map Injectivity

PrivateLabels unavailable

Private saving unavailable

Multiple integration and change of variablesMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010420Repair a doubled integral caused by a two-to-one coordinate map

View access options

Mvc Change OF Variables MultiplicityMvc Map Hypothesis Audit

PrivateLabels unavailable

Private saving unavailable

Multiple integration and change of variablesMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010517Compute an ellipse circulation two independent ways

View access options

Mvc Planar Line IntegralsMvc Greens Theorem

PrivateLabels unavailable

Private saving unavailable

Vector fields, line integrals, and Green's theoremMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010518Check outward flux across a parabolic cap

View access options

Mvc Green Flux FormMvc Curved Boundary Orientation

PrivateLabels unavailable

Private saving unavailable

Vector fields, line integrals, and Green's theoremMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010617Orient a triangular Stokes calculation

View access options

Mvc Stokes TheoremMvc Surface Boundary Orientation

PrivateLabels unavailable

Private saving unavailable

Surface integrals, divergence theorem, and Stokes' theoremMultivariable and Vector Calculus · Mixed review

Progress not loaded

MVC:010618Balance flux across a capped paraboloid

View access options

Mvc Divergence TheoremMvc Oriented Flux Graphs

PrivateLabels unavailable

Private saving unavailable

Surface integrals, divergence theorem, and Stokes' theoremMultivariable and Vector Calculus · Mixed review

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917011Let \mathbf v=\langle 6,-2,3\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917012A particle is acted on by the constant force \mathbf F=\langle 4,-2,5\rangle, measured in newtons.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917013Let \mathbf u=\langle 2,-1,3\rangle and \mathbf v=\langle 1,4,-2\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917014Let \mathbf u=\langle 1,2,2\rangle and \mathbf v=\langle 2,1,-2\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917015Let A=(1,1,1), B=(2,3,4), and C=(0,2,3).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917016Let \mathbf u=\langle 2,0,1\rangle, \mathbf v=\langle 1,3,0\rangle, and \mathbf w=\langle 0,1,4\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917017The diagonals of a parallelogram in \mathbb R^3 are the vectors \mathbf d_1=\langle 3,1,2\rangle and \mathbf d_2=\l…

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917018A line L passes through the points A=(3,-1,2) and B=(5,3,1).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917019For each pair of lines below, determine whether the lines are identical, distinct and parallel, intersecting but no…

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917020Let P=(1,2,3), and let L be the line through A=(0,1,1) and B=(2,3,0).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917021Let P=(1,0,-1), Q=(2,1,3), and R=(3,-1,1).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917022Consider the planes (a) For each of \Pi_2, \Pi_3, and \Pi_4, determine whether the plane is parallel to \Pi_1, perp…

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917023Let L be the line given by \mathbf r(t)=\langle 1,0,2\rangle+t\langle 2,-1,2\rangle, and let \Pi be the plane x+2y-…

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917024Let P=(3,-1,2) and let \Pi be the plane 2x-2y+z=5.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917025Consider the planes x-2y+2z=4 and -2x+4y-4z=6.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917026Let L_1 be the line x=1+t, y=t, z=2-t, and let L_2 be the line x=2s, y=1-s, z=s.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917027Let \Pi_1 be the plane x+y-z=2 and let \Pi_2 be the plane 2x-y+z=1.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917028Let L be the line given in symmetric form by and let P=(1,1,1).

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917029By completing the square, rewrite in standard form.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917030Identify each of the following surfaces.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917031Let for all real t at which the expression is defined as a vector in \mathbb{R}^{3} with t\neq 2.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917032Let C be the curve of intersection of the circular cylinder x^{2}+y^{2}=16 and the plane z=x-2y+3.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917033Let C be the intersection of the sphere x^{2}+y^{2}+z^{2}=9 and the plane z=1.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

MVC:9917034Let \mathbf{r}(t)=\langle t^{2}-t,\ e^{2t},\ \cos t\rangle.

View access options

Geometry Vector FunctionsMultivariable Vector Calculus Problem Solving

PrivateLabels unavailable

Private saving unavailable

Geometry, vectors, and vector-valued functionsMultivariable and Vector Calculus · Calculation

Progress not loaded

Problem results

MVC:9917001Let A=(1,-2,4) and B=(5,2,-2).

MVC:9917002Describe geometrically the set of points (x,y,z) in \mathbb R^3 determined by each of the following.

MVC:9917003Let P=(-2,3,6).

MVC:9917004A sphere has center C=(2,-1,3) and passes through the point P=(4,1,0).

MVC:9917005Find an equation of the sphere whose center lies on the z-axis and which passes through both A=(2,1,1) and B=(1,-2,2).

MVC:9917006Let A=(2,0,-1), B=(-1,3,2), and C=(4,-2,5).

MVC:9917007Let A=(1,0,1), B=(3,2,2), and C=(0,3,4).

MVC:9917008Let \mathbf u=\langle 1,-1,2\rangle and \mathbf v=\langle 2,1,1\rangle.

MVC:9917009Let \mathbf u=\langle 2,1,-2\rangle and \mathbf v=\langle -1,2,1\rangle.

MVC:9917010Let \mathbf a=\langle 1,2,2\rangle and \mathbf b=\langle 3,1,-1\rangle.

Find a problem

Problem results

MVC:9917001Let A=(1,-2,4) and B=(5,2,-2).

MVC:9917002Describe geometrically the set of points (x,y,z) in \mathbb R^3 determined by each of the following.

MVC:9917003Let P=(-2,3,6).

MVC:9917004A sphere has center C=(2,-1,3) and passes through the point P=(4,1,0).

MVC:9917005Find an equation of the sphere whose center lies on the z-axis and which passes through both A=(2,1,1) and B=(1,-2,2).

MVC:9917006Let A=(2,0,-1), B=(-1,3,2), and C=(4,-2,5).

MVC:9917007Let A=(1,0,1), B=(3,2,2), and C=(0,3,4).

MVC:9917008Let \mathbf u=\langle 1,-1,2\rangle and \mathbf v=\langle 2,1,1\rangle.

MVC:9917009Let \mathbf u=\langle 2,1,-2\rangle and \mathbf v=\langle -1,2,1\rangle.

MVC:9917010Let \mathbf a=\langle 1,2,2\rangle and \mathbf b=\langle 3,1,-1\rangle.