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 Hand Rule.

If we let the angle between A and B be , then the cross product of A and B can be expressed as

    A x B = A B sin()

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
Further, if you are familiar with determinants, A x B, is 
Comparing Figures 1 and 2, we notice that 
    A x B = - B x A

    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

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