Mechanics:AS level Hinge force problem!I got stuck at part c+d.

A uniform rod AB of weight 12N is free to turn in a vertical plane about a smooth hinge at its upper end A.It is held at an angle theta to the vertical by a force P acting at B.

a)P is 5N applied horizontally.What is the force at the hinge?

b)P is horzontal and theta is arctan 3/4.What is the force at the hinge?

c)P is at right angles to AB and of magnitude 3N.What is the force at the hinge?

d)P is at right angles to AB and theta is arctan 3/4.Find P and the hinge force.

__Answers:__

a)13N

b)12.8N

c)3underroot3 N

d)3.6N ; 10.25N