The vector (or cross) product of the vectors a and b is defined to be:
a \times b = |a| |b| \sin \theta \hat{n}
where \theta is the angle between the vectors and \hat{n} is a unit vector perpendicular to both a and b.
The direction of \hat{n} is given by the right-hand rule - see the diagram.

The magnitude the cross product is equal to the area of the parallelogram that the vectors span.


If i, j and k are the familiar unit vectors, then:
i \times j = k, j \times k = i, k \times i = j and
i \times i = 0, j \times j = 0, k \times k = 0

If a = a_1i+a_2j+a_3k \quad and b = b_1i+b_2k+b_3k \quad then: a \times b = (a_2b_3-a_3b_2)i + (a_3b_1-a_1b_3)j + (a_1b_2-a_2b_1)k