1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal unit vectors.]

A particle \(P\) of mass 2 kg moves under the action of two forces, \(( p \mathbf { i } + q \mathbf { j } ) \mathrm { N }\) and \(( 2 q \mathbf { i } + p \mathbf { j } ) \mathrm { N }\), where \(p\) and \(q\) are constants. Given that the acceleration of \(P\) is \(( \mathbf { i } - \mathbf { j } ) \mathrm { ms } ^ { - 2 }\)

1. find the value of \(p\) and the value of \(q\).
2. Find the size of the angle between the direction of the acceleration and the vector \(\mathbf { j }\). At time \(t = 0\), the velocity of \(P\) is \(( 3 \mathbf { i } - 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\)
   At \(t = T\) seconds, \(P\) is moving in the direction of the vector \(( 11 \mathbf { i } - 13 \mathbf { j } )\).
3. Find the value of \(T\).