Torque, have answer, need explanation

[gvcalamike]

Force F= (2.0N)i - (3.0N) k acts on a pebble with position vector r= (0.50m)j - (2.0m)k relative to the origin. In unit vector notation, what is the resulting torque about a) the origin and b) the point (2.0m, 0, -3.0m)?

Okay, I got the answers and their right. For both (-1.5)i - (4.0)j -(1.0) k Nm. My question is what is the relation here? Why is the torque the same about the origin and a point? Is it because the position doesn't affect the torque, but the force does? What am I missing because I want to know the relationship here or if it's pure coincidence.

 

[Dick]

Force F= (2.0N)i - (3.0N) k acts on a pebble with position vector r= (0.50m)j - (2.0m)k relative to the origin. In unit vector notation, what is the resulting torque about a) the origin and b) the point (2.0m, 0, -3.0m)?

Okay, I got the answers and their right. For both (-1.5)i - (4.0)j -(1.0) k Nm. My question is what is the relation here? Why is the torque the same about the origin and a point? Is it because the position doesn't affect the torque, but the force does? What am I missing because I want to know the relationship here or if it's pure coincidence.

It happens to work that way because P=[2m,0,-3m] happens to be parallel to the force F=[2N,0,-3N]. So Fx(r-P)=Fxr-FxP and FxP is zero since F and P are parallel. So Fx(r-P)=Fxr. Position generally does affect the torque. But not in this case.

 

[gvcalamike]

Thank you sir.