3
\includegraphics[max width=\textwidth, alt={}, center]{d1eb99a1-04e5-43bc-87b4-d0f7c962135c-2_599_677_1151_696} A uniform beam \(A B\) of mass 15 kg and length 4 m is freely hinged to a vertical wall at \(A\). The beam is held in equilibrium in a horizontal position by a light rod \(P Q\) of length \(1.5 \mathrm {~m} . P\) is fixed to the wall vertically below \(A\) and \(P Q\) makes an angle of \(30 ^ { \circ }\) with the vertical (see diagram). The force exerted on the beam at \(Q\) by the rod is in the direction \(P Q\). Find

1. the magnitude of the force exerted on the beam at \(Q\),
2. the magnitude and direction of the force exerted on the beam at \(A\).