A second way to multiply vectors is to take the cross product, which results in a vector perpendicular to the two vectors in the cross product. An example is a torque:

τ = r × F

The magnitude of the resultant vector is r F sin(θ).

The direction is given by the right-hand rule. Using your right hand, point your fingers in the direction of the first vector (r), curl them into the direction of the second vector (F), and your thumb, sticking out, will point in the direction of the resultant vector.

Note that the cross product is ...

• zero when the vectors are parallel
• maximum when the vectors are perpendicular to one another

Note also that a × b = - b × a.

c = a × b = (a_y b_z - b_y a _z) + (a_z b_x - b_z a_x) + (a_x b_y - b_x a_y)