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Calculus 3: 3D Space

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All Calculus 33D SpaceVector FunctionsDot and cross productEquations of lines and planesParametric curves, conic sectionsTangent vectors and arc lengthCylinders and quadric surfacesIntegrals of vector functionsArc length and curvatureMultivariable functionsSurface parameterizationPartial derivativesLinearization, chain rule, gradientTangent planes and linear approximationsOptimizationLagrange multipliersDouble integralsTriple integralsChanging coordinates for integrationSurface areaVector fields, divergence, and curlLine integralsGreen's TheoremFluxStokes' TheoremDivergence TheoremComplex numbers
Symmetric Equations for Line of Intersection of Two Planes

Consider the planes x + y + z = 1 and x - 2y + 3z = 1

a. Find the angle between the two planes

b. Find symmetric equations for the line of intersection of the two planes

3D SpaceMediumVideo
Topographical Map Route Planning for Winter Sports

Using a topographical map, analyze the contours to plan a route through the mountains with minimal elevation changes. Discuss the importance of this analysis in winter sports like skiing or snowshoeing.

3D SpaceMediumVideoNeeds Attention
Assessing Axis Variation in 3D Graphs for RightHand Rule

Solve problems involving different variations of axes given a three-dimensional graph and assess the suitability of the axis variation for the right-hand rule.

3D SpaceMediumVideoNeeds Attention