The points \(C\) and \(D\) are at a distance \(( 2 \sqrt { } 3 ) a\) apart on a horizontal surface. A rough peg \(A\) is fixed at a vertical distance \(6 a\) above \(C\) and a smooth peg \(B\) is fixed at a vertical distance \(4 a\) above \(D\). A uniform rectangular frame \(P Q R S\), with \(P Q = 3 a\) and \(Q R = 6 a\), is made of rigid thin wire and has weight \(W\). It rests in equilibrium in a vertical plane with \(P S\) on \(A\) and \(S R\) on \(B\), and with angle \(S A C = 30 ^ { \circ }\) (see diagram).

1. Show that \(A B = 4 a\) and that angle \(S A B = 30 ^ { \circ }\).
2. Show that the normal reaction at \(A\) is \(\frac { 1 } { 2 } W\).
3. Find the frictional force at \(A\).