What is the direction of torque when n is not perpendicular to r?

[Aziza]

My book defines the general formula for torque as:

n.(r×F), where . means dot product, n is a unit vector along the line about which you are taking the torque, F is the force acting at some point, and r is the vector from the line to the point at which the force acts. So I know that when the line about which you are taking the torque is perpendicular to r, then the torque is defined as r×F, so it has a direction perpendicular to r and F.

However, what would be the direction of the torque if n is not perpendicular to r? n.(r×F) does not reveal the direction since it is just a scalar. Would the direction still be just r×F in this general case?

 

[Aziza]

nvm i think i just answered my question...if you just consider the torque about each axis then its obvious that the direction of the torque is just the direction of r×F

 

[tiny-tim]

Hi Aziza!

Yes, what your book defines as the torque about an axis is really the component of the torque along that axis.