Three forces, "F1", "F2" and "F3", act on a support fixed in a wall as shown in Fig. 1. Using the vector analysis method :

a) Calculate the value of the Cartesian components of each force.

b) Calculate the Cartesian (Rx, Ry) and polar (magnitude and direction) components of the resultant "R" of these three forces.

c) Considering that the support can be assimilated to a point, calculate the force exerted by the wall on the support which is subjected to the 3 forces so that the support remains in place.

d) A force "F4" is added to the support. Calculate the size and direction of force "F4" so that the combination of the 4 forces is equal to :

10.0i+ 55.0j = 2F1 - F2 + 0.5*F3 + F4??

e) Draw "F4" and "R" in the (x,y) axis system. Identify the magnitude and orientation of each vector.