3. At time \(t\) seconds, a particle \(P\) has position vector \(\mathbf { r }\) metres relative to a fixed origin \(O\), where
$$\mathbf { r } = \left( t ^ { 3 } - 3 t \right) \mathbf { i } + 4 t ^ { 2 } \mathbf { j } , t \geq 0$$
Find
- the velocity of \(P\) at time \(t\) seconds,
- the time when \(P\) is moving parallel to the vector \(\mathbf { i } + \mathbf { j }\).
(5)