A single force of 14 kN acts on a bracket that is fixed to a wall. What is the total moment in vector format at point A due to the force?

To find moment about a point, the position vector from the point of interest to any point on the force line of action is crossed with the force vector. In equation form this is

     M_A = r × F

Position Vector r from Point A to the
Force Line of Action

For this problem, the position vector is drawn from point A to point E giving

     r_AE = 6i - k

Another position could be used, such from A to D.

The force vector can be determined by multiply its magnitude with its unit directional vector. The location of point D and E is (8,8,2) and (6,0,5) respectively. The force vector is

     F = F u_DE
    
       = -3.191i - 12.764j + 4.786k

Substituting into the cross product gives,

This determinate can be evaluated as,

    M_A = -12.76i - 25.52j - 76.58k