## Abstract

The The ordered set of vectors { and so the vector product is not commutative.

*vector product*(often called the cross product) of two vectors**a**and**b**, denoted by**a**×**b**, or sometimes**a**∧**b**, 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)

**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)

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## Copyright information

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