# cross product

(2.3 hours to learn)

## Summary

The cross product is an operation which takes to vectors and returns another vector orthogonal to both. It is commonly used to answer geometric questions involving points, lines, and planes, and to compute volumes.

## Context

This concept has the prerequisites:

- vectors (The cross product is an operation on vectors.)
- dot product (The cross product is often used in conjunction with the dot product.)

## Goals

- Know the definition and basic properties of the cross product

- Know the "right-hand rule" for cross products

- Know the formula for the cross product in terms of the lengths of two vectors and the angle between them.

- Be able to compute the volume of a prism using the dot product and cross product

## Core resources (read/watch one of the following)

## -Free-

→ Khan Academy: Linear Algebra

- Lecture "Cross product introduction"
- Lecture "Proof: relationship between cross product and sin of angle"
- Lecture "Dot and cross product comparison/intuition"
- Lecture "Vector triple product expansion"

## Supplemental resources (the following are optional, but you may find them useful)

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 5.3, subsection "The cross product," pages 275-277

Additional dependencies:

- determinant

## See also

- The cross product can be generalized to other dimensions using k-forms .