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 certain point is found to be zero, does this mean that it is necessarily zero about any arbitrary point ?

Explanation

NO , not necessarily . ltbr Given `sum _(i)F_(1)ne0`
the sum of torques about a certain point O,`sum _(i)r_(1)xxF_(j)=0`
the sum of torques about any other point O'
`sum _(i)(r_(j)-a)xxF_(j)=sum_(i)r_(j)xxF_(j)-axxsum_(i)F_(i)`
Here , the second term need not vanish.
Therefore , sum of all the torque about any arbitrary point need not be zero necessarily.