5. A particle of mass 2 kg is moving under the action of a force \(\mathbf { F N }\) which, at time \(t\) seconds, is given by $$\mathbf { F } = 4 t \mathbf { i } - \sqrt { t } \mathbf { j } + 6 \mathbf { k }$$ When \(t = 1\), the velocity of the particle is \(\left( 3 \mathbf { i } - \frac { 1 } { 3 } \mathbf { j } - \mathbf { k } \right) \mathrm { ms } ^ { - 1 }\).

1. Find an expression for the velocity vector of the particle at time \(t \mathrm {~s}\).
2. Determine the values of \(t\) when the particle is moving in a direction perpendicular to the vector \(( - \mathbf { i } + 3 \mathbf { k } )\).