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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
Equations of lines and planes

1. Find a vector and parametric equations for the line that passes through (4,2) and is parallel to v = <-1,5>. Then find 2 other points on that line.

2. Find parametric equations for the line segment joining points P(2, -4, -1) and Q(5, 0, 7). Where does this line intersect the xy-plane?

3D SpaceEasyVideo
3D Coordinate System

Plot the point B(−2,−4,−3)B(-2,-4,-3) in the 3D coordinate system.

3D SpaceEasyVideo
Line Through Points in 3D Space

Find the line through the points (5, -2, 3) and (7, 4, 1)

3D SpaceEasyVideo
Plotting Points in Three Dimensional Coordinate Systems

Plot the point P(2,4,3)P(2, 4, 3) in the 3D coordinate system.

3D SpaceEasyVideo
Graphing a Sphere in 3D Space

Using the equation of a sphere, x2+y2+z2=1x^2 + y^2 + z^2 = 1, graph the sphere with the given axes.

3D SpaceEasyVideo