Vector Product (cont.1)

Perhaps the most startling result of the vector product definition is that A x B and B x A are not equal; in fact, A x B =-B x A. In mathematical language, vector multiplication is not commutative.(Recall that matrix multiplication is also not commutative.)
Just as for the scalar product, we need to know what the vector products of the unit vector are. we find that
i x i = 0. Evaluating the cross products of the other unit vectors similarly, we have

i x i = j x j = k x k = 0

i x j = k, j x k = i, k x i = j

To write A x B in component form we need the distributive law, namely A x (B+C) =A x B + A x C. It is not difficult but very tedious to prove this law, so we shall assume and use it without proof.Then we have



See also:Determinant


Next: Example 3.