What Are the Vertical and Horizontal Forces on Door Hinges?

[issisoccer10]

Homework Statement

A door with weight Mg has a horizontal width W and a vertical length L. There are two hinges that hold up the door along the right side of the door. The top hinge is a distance d from the top of the door and the bottom hinge is a distance d from the bottom of the door. What are the vertical and horizontal forces on each of the hinges?

Homework Equations

∑F = 0
∑τ = 0

The Attempt at a Solution

As for the horizontal forces, I believe that using torques, based on the the force on the upper hinge, F * (L-2d) = Mg(W/2). Then the horizontal force on the lower hinge would just be equal to that but in the opposite directon.
However, as for the vertical components, I'm a little stuck. Some similar questions have been asked in these forums, but they all seem to say something along the lines of "each hinge supports the weight of the hinge equally" or "only the top hinge supports the weight of the door." Yet my question does nothing of the sort. How should I go about finding the vertical components of the doors? I have the same question as for which direction each of the horizontal compontent of the hinges point. Is there a right or wrong answer for their direction, as long as they are opposite, since there is no indication in the question?

 

[BishopUser]

the direction of the horizontal forces is easy to visualize. the bottom hinge tries to push the door away and the top one tries to pull it back. as for the vertical forces i think you assume that each one is mg/2