4. The force \(\mathbf { F } _ { \mathbf { 1 } } = ( 5 \mathbf { i } + 2 \mathbf { j } ) \mathrm { N }\) acts at the point \(A\) on a lamina where the position vector of \(A\), relative to a fixed origin \(O\), is \(( 3 \mathbf { i } - 2 \mathbf { j } ) \mathrm { m }\).
- Calculate the magnitude and the sense of the moment of the force about \(O\).
Another force \(\mathbf { F } _ { 2 } = ( p \mathbf { i } + q \mathbf { j } )\), acts at the point \(B\) with position vector ( \({ } ^ { - } \mathbf { i } + 4 \mathbf { j }\) ) m so that the resultant moment of the two forces, \(\mathbf { F } _ { 1 }\) and \(\mathbf { F } _ { 2 }\), about \(O\) is zero.
Given also that the moment of \(\mathbf { F } _ { 2 }\) about \(A\) is 34 Ns in a clockwise sense,
- find the values of \(p\) and \(q\).