The vector sum of a system of non-collinear forces acting on a rigid body is given to be non-zero. If the vector sum of all torques due to the system of forces about a centain point is found to be zero, does this mean that it is necessarily zero about any arbitrary point ?

Explanation

No, not necessary.
We are given that `underset (i) sum overset rarr(F_(i)) !=0`.
However, the sum of torque about a centrain point `O, underset (i)sum overset rarr(r_(i))xx overset rarr(F_(i)) =0`
About any other point O', the sum of torque would be `underset (i)sum (overset rarr(r_(i))-overset rarr(a)) xx overset rarr(F_(i))= underset (i)sum overset rarr(r_(i)) xx overset rarr(F_(i)) - overset rarr(a) xx underset (i)sum overset rarr(F_(i))`
At the second term need not vanish for any value of `overset rarr(a)`, therefore, sum of all the torques about any arbitrary point need not be zero necessarily.