- The position vector, \(\mathbf { r }\) metres, of a particle \(P\) at time \(t\) seconds, relative to a fixed origin \(O\), is given by
$$\mathbf { r } = ( t - 3 ) \mathbf { i } + ( 1 - 2 t ) \mathbf { j }$$
- Find, to the nearest degree, the size of the angle between \(\mathbf { r }\) and the vector \(\mathbf { j }\), when \(t = 2\)
- Find the values of \(t\) for which the distance of \(P\) from \(O\) is 2.5 m .