Vectors pp 56-61

# The vector product

• Tony Bridgeman
• P. C. Chatwin
• C. Plumpton
Chapter
Part of the Core Books in Advanced Mathematics book series (CBAM)

## Abstract

The vector product (often called the cross product) of two vectors a and b, denoted by a × b, or sometimes ab, is defined to be a vector of magnitude |a| |b| sin θ, where θ is the angle contained between a and b, with the direction of a × b being perpendicular to both a and b in the sense in which a right-handed corkscrew moves when rotated from a to b. Thus if n is a unit vector in this direction (see Fig. 6.1)
$$a\times b=\left( {\left| a \right|\left| b \right|\sin \theta } \right)n.$$
(6.1)
The ordered set of vectors {a, b, n} is said to be a right-handed set. (This is because of the way in which the direction of n is defined.) As {b, a, −n} is also a right-handed set of vectors, it follows that
$$a\times b=-b\times a$$
(6.2)
and so the vector product is not commutative.

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## Copyright information

© Tony Bridgeman, P. C. Chatwin and C. Plumpton 1983

## Authors and Affiliations

• Tony Bridgeman
• 1
• 2
• P. C. Chatwin
• 1
• 2
• C. Plumpton
• 1
1. 1.University of London School Examinations DepartmentUK
2. 2.University of LiverpoolUK