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

A particle \(A\) has mass 3 kg and a particle \(B\) has mass 2 kg .
The particles are moving on a smooth horizontal plane when they collide directly.
Immediately before the collision, the velocity of \(A\) is \(( 3 \mathbf { i } - \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) and the velocity of \(B\) is \(( - 6 \mathbf { i } + 2 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) Immediately after the collision the velocity of \(A\) is \(\left( - 2 \mathbf { i } + \frac { 2 } { 3 } \mathbf { j } \right) \mathrm { ms } ^ { - 1 }\)

1. Find the total kinetic energy of the two particles before the collision.
2. Find, in terms of \(\mathbf { i }\) and \(\mathbf { j }\), the impulse exerted on \(A\) by \(B\) in the collision.
3. Find, in terms of \(\mathbf { i }\) and \(\mathbf { j }\), the velocity of \(B\) immediately after the collision.