How Do I Find the Tension in the Cable AB Given Forces and Angles?

[jlhannah]

(Figure is attached) Find the tension in the cable AB such that the net moment about the hinge axis CD induced by the forces F and P is zero. The force F is applied at point A and the force P is applied at point E. The magnitude of the force P is P = 65 lb. Two coordinate direction angles for the force P are known: beta = 37 degrees and gamma = 165 degrees. The hinged plate is rectangular.

- I found the unit vector CD {0i + 0.8j + 0.6k}
- I know that the force vector will be F(ab){-0.43i + 0.29j + 0.86k}

How do I find the third coordinate direction angle for the force P?
From there, what radius do I use for my cross product? I can pick any point on the line of action CD, correct?

 

[mfb]

What is the definition of $\beta$ and $\gamma$?
They are related to the direction of P somehow.

From there, what radius do I use for my cross product? I can pick any point on the line of action CD, correct?

The one closest to the point where P acts.