Cross Product

Geometrically, the cross product of two vectors is the parallelogram between them.

The Cross Product is one of the ways that vectors can be multiplied together.

The cross product of two vectors in a 3D space is shown below. We might add that calculation has unit vectors included. See Appendix A for more about this.

Define vectors u and v as:

$\vec u = (a,b,c)$
$\vec v = (d,e,f)$

If you know how to calculate determinants then you’ll probably notice that the above is done the same way as the calculation of a 3×3 determinant.

$\vec u \times \vec v = \begin{vmatrix} \hat i & \hat j & \hat k \\ a & b & c \\ d & e & f \end{vmatrix} = [bf - ec]\hat i + [cd-fa]\hat j +[ae-db]\hat k$

It is probably better to see it done this way because then you see that unit vectors i,j,k are involved:

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