Vectors, lines, planes and curves in spaceReading · 0%
Partial derivatives, gradients and tangent planes1 h 15 min of study
Optimization in several variables and Lagrange multipliers1 h of study
Double and triple integrals and change of variables1 h 20 min of study
Line and surface integrals and the theorems of vector calculus1 h 20 min of study

This unit is ≈15% of the GRE Math, across 5 lessons. Full syllabus

Lesson 1 of 5 · Calculus III: multivariable and vector calculus

Vectors, lines, planes and curves in space

3 quick checks≈3% of the testCore: Core: tested on most papers

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By the end you’ll be able to

Compute dot and cross products and use them for angles, projections, areas of parallelograms and triangles, and volumes via the scalar triple product
Write equations of lines and planes; find intersections, angles and distances (point to plane, point to line, between skew lines)
Identify cylinders and quadric surfaces (ellipsoids, paraboloids, hyperboloids, cones) from their equations

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Adaptive questions on vectors, lines, planes and curves in space.

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Analyse vector-valued functions: velocity, acceleration, unit tangent vector, arc length and curvature

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