16 Two particles, \(P\) and \(Q\), move in the same horizontal plane.
Particle \(P\) is initially at rest at the point with position vector \(( - 4 \mathbf { i } + 5 \mathbf { j } )\) metres and moves with constant acceleration \(( 3 \mathbf { i } - 4 \mathbf { j } ) \mathrm { ms } ^ { - 2 }\)
Particle \(Q\) moves in a straight line, passing through the points with position vectors \(( \mathbf { i } - \mathbf { j } )\) metres and \(( 10 \mathbf { i } + c \mathbf { j } )\) metres.
\(P\) and \(Q\) are moving along parallel paths.
16
- Show that \(c = - 13\)
16 - Find an expression for the position vector of \(P\) at time \(t\) seconds.
16
- (ii) Hence, prove that the paths of \(P\) and \(Q\) are not collinear.