A force of -F i acts at the origin of the coordinate system. The torque about the point (0,1,-1) is:

Step-by-step solution

The torque about a point P due to a force F acting at a point A is given by = r F , where r is the position vector of the point of application A relative to the point P . The point of application is A = (0, 0, 0) . The point about which torque is calculated is P = (0, 1, -1) . The position vector r of A relative to P is r = A - P = (0 - 0) i + (0 - 1) j + (0 - (-1)) k = - j + k . The force vector is F = -F i . The torque is = (- j + k ) (-F i ) = F( j i ) - F( k i ) . Using the cross product relations j i = - k and