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# The Cross Product of Two Vectors in Space

## Lecture no. 10 from the course: Understanding Multivariable Calculus: Problems, Solutions, and Tips

Taught by Professor Bruce H. Edwards | 29 min | Categories: The Great Courses Plus Online Mathematics Courses

Take the cross product of two vectors by finding the determinant of a 3x3 matrix, yielding a third vector perpendicular to both. Explore the properties of this new vector using intuitive geometric examples. Then, combine it with the dot product from Lecture 9 to define the triple scalar product, and use it to evaluate the volume of a parallelepiped.

## 36 Lectures

1

A Visual Introduction to 3-D Calculus

0 of 33 min

2

Functions of Several Variables

0 of 30 min

3

Limits, Continuity, and Partial Derivatives

0 of 30 min

4

Partial Derivatives—One Variable at a Time

0 of 30 min

5

Total Differentials and Chain Rules

0 of 31 min

6

Extrema of Functions of Two Variables

0 of 30 min

7

Applications to Optimization Problems

0 of 30 min

8

Linear Models and Least Squares Regression

0 of 31 min

9

Vectors and the Dot Product in Space

0 of 29 min

10

The Cross Product of Two Vectors in Space

0 of 29 min

11

Lines and Planes in Space

0 of 31 min

12

Curved Surfaces in Space

0 of 31 min

13

Vector-Valued Functions in Space

0 of 31 min

14

Kepler’s Laws—The Calculus of Orbits

0 of 30 min

15

Directional Derivatives and Gradients

0 of 30 min

16

Tangent Planes and Normal Vectors to a Surface

0 of 28 min

17

Lagrange Multipliers—Constrained Optimization

0 of 30 min

18

Applications of Lagrange Multipliers

0 of 29 min

19

Iterated integrals and Area in the Plane

0 of 30 min

20

Double Integrals and Volume

0 of 29 min

21

Double Integrals in Polar Coordinates

0 of 30 min

22

Centers of Mass for Variable Density

0 of 29 min

23

Surface Area of a Solid

0 of 31 min

24

Triple Integrals and Applications

0 of 29 min

25

Triple Integrals in Cylindrical Coordinates

0 of 30 min

26

Triple Integrals in Spherical Coordinates

0 of 29 min

27

Vector Fields—Velocity, Gravity, Electricity

0 of 30 min

28

Curl, Divergence, Line Integrals

0 of 31 min

29

More Line Integrals and Work by a Force Field

0 of 31 min

30

Fundamental Theorem of Line Integrals

0 of 31 min

31

Green’s Theorem—Boundaries and Regions

0 of 30 min

32

Applications of Green’s Theorem

0 of 30 min

33

Parametric Surfaces in Space

0 of 32 min

34

Surface Integrals and Flux Integrals

0 of 31 min

35

Divergence Theorem—Boundaries and Solids

0 of 29 min

36

Stokes’s Theorem and Maxwell's Equations

0 of 33 min

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