The distance from to the point where takes effect is . is in the x-y plane, so . The momentum will then be
Now, we probably want to charge the support at as much as possible, so we set . Besides, we want and to be orthogonal to each other, so
, so is already in the x-y plane.
So we could parametrisize and write , implying that , which means that could have basically any non-negative length.
Now we know that there exist with the in the x-y plane with the length 970 N, orthogonal to . Let's use that in our momentum formula:
, where is the angle between and
Now, since and are orthogonal, , so , which should be the maximum magnitude of the momentum.
Alternativelly, you could turn into poolar coordinates:
perform the cross product between and to get the momentum, extract the magnitude of the momentum (the vector lenth), and analyse the expression to se which that gives the greatest magnitude of the momentum or to directly extract the greatest value of the expression.