Vector Product

The vector product (or "cross product") of two vectors A and B is defined as:

A x B = C

The resulting vector C then has the cartesian components:

C_x = A_y B_z - A_zB_y

C_y = A_z B_x - A_xB_z

C_z = A_x B_y - A_yB_x

The applet above lets you play with this concept. With the sliders on the right, you can adjust the lengths of the vectors, r, as well as their angles relative to the z-axis, theta, and x-axis, phi. The cross product is calculated automatically and then displayed. The whole operation works, of course, only in three spatial dimensions. To give a more precise indication of the location of the vectors in 3-d, we show their projections into the xy plane as well.