In a past paper I came across this question which I tried very hard to solve with no luck:

The moment vector M of a vector B about the point A is found by the formula:

M = r x B

where r is the vector from point A to the position where vector B is applied.

A force F = 3i - 4j + k Newtons act at P, having co-cordinates (-2,3,5) meters.

a) Find the moment vector of force F about point A, having co-ordinates (0,-1,-3), and hence find the magnitude of this moment.

r = -2i + 4j - 8k

|M| = 44.45Nm

b) Find two possible points R1 and R2, both having equal y and z co-ordinates, around which the magnitude of the moment of the same force F is maximum and that are at a distance $\displaystyle 5\sqrt{3}$ meters from point P.

I deduced that the line passing through R1 and R2 has perpendicular to the force (for it to be max). I tried to prove with dot product of line (R1R2) with the Force F. Would it be a good idea to try working with point P on the same line of R1 and R2 as long as they are at the mentioned distance from point P. attached.