|The cross product, also called the vector product, is an
operation on two vectors. The cross product of two vectors produces a third
vector which is perpendicular to the plane in which the first two lie.
That is, for the cross of two vectors, A and B, we place
A and B so that their tails are at a common point. Then,
their cross product, A x B, gives a third vector, say C,
whose tail is also at the same point as those of A and B.
The vector C points in a direction perpendicular (or normal) to
both A and B. The direction of C depends on the Right
If we let the angle between A and B be , then the cross product of A and B can be expressed as
Figure 1 A x B = C
|If the components for vectors A and B are
known, then we can express the components of their cross product, C
= A x B in the following way
Cx = AyBz - AzBy
Cy = AzBx - AxBz
Cz = AxBy - AyBx
A very nice simulation which allows you to investigate the properties of the cross product is available by clicking HERE. Use the "back" button to return to this place.
Figure 2 B x A = D