Is Torque Equal on All Axes When a Rigid Body's Net Force Is Zero?

[miss photon]

Homework Statement

prove that when the net force on a rigid body is zero, the torque about any line perpendicular to the plane of the forces is equal.

Homework Equations

\tau=I\alpha

The Attempt at a Solution

it is known that angular velocity, and hence angular acceleration about any line is the same for a given rotating rigid body.
implies, \alpha is same about all lines.
if we accept the above statement to be true, then I comes out to be equal about every axis, which is a contradiction.

 

[Feldoh]

If it's perpendicular the the cross-product will just be tau = |r||F|