I know how to get G but I couldnt understand how to get Mome

I know how to get G but I couldn\'t understand how to get Moment G.

I know Moment is Fx d , and that\'s why it shows multiplication of each vector component.

but I couldn\'t understand why 50 it has different mark which are +,- .

plz explain for me!!!

Solution

M = r X F (not F X r)

1. For the first force of 50 kN at screw A: (Draw the top view of the picture to understand -5i)

r = -5i-7k (+,- Sign conventions according to co-ordinate system)

F = -50j

r X F = -350i+250k ------1

2. For the force 50 kN at screw B

r= 5i-7k and F = 50j

r X F = 350i+250k -----2

3. For the force 8 kN at C

r= 40j-6k and F=-8i

r X F = 48j + 320k -----3

Adding three equations we get

M = 48j+820k