Sometimes an example can be worth a thousand words (especially in physics).
Consider a rectangular body (represented by periods), that is acted on by a force F, and free to rotate about the point O.
Code:
......---> F
. .
. .
. .
O.....
There are two ways to go about computing torque (which lead to the same thing). Torque = Force * moment arm. So to form the "moment arm", construct a "line of force" (a line paralell to the force vector), and drop a perpindicular line down to the point of rotation. This "perpindicular" is the moment arm, labeled 'm' below. The magnitude of the torque is therefore this value m multiplied by the magnitude of the force (torque = Fm). Note that this is a scalar equation.
Code:
---------> F
| .
m | .
| .
O.....
Alternatively, you could construct a vector whose initial point corresponds to O, the point of rotation, and whose final point corresponds to the point of application of the force F. You would then take the cross product of the
vector F and the "OF" vector. Note that this is a vector equation.