statics – finding a moment of a force in xyz plane

1. The problem statement, all variables and given/known data

I attached the question.

2. Relevant equations

M = r x F
M = F x d
Resolving forces, Fx/Fy/Fz = F cos/sin theta (depending on which angle you take)

3. The attempt at a solution

I can easily find the moment of the 100 N and 120 forces, but I’m having trouble finding the moment of the 80 N force. I know we use r x F, but getting the r and F vectors is a problem for me. Here is my attempt:

Fx = -80 cos 20 = -75.18
Fy = 80 sin 20 cos 60 = 13.68
Fz = 80 sin 20 sin 60 = 23.70

F = (-75.18i + 13.68j + 23.70k)

Rx = 0, to get Ry and Rz I made a triangle with the 180mm length and 30 degree angle.

Ry = 180 cos 30 = 155.88
Rz = -180 sin 30 = -90

R = (0, 155.88, -90)

M = r x F

When I take the cross product I get = { 4923.9972, 6766.2, 11719.0584 }

While the actual answer is { 0, -6770, 1172 }

Where did I make the mistake?

Attached Images
File Type: png toughone.png (30.2 KB)

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