In this question lengths are in centimetres and time, \(t\), is in seconds.
A particle \(P\) is moving in a straight line with a speed of 26 in the direction of the vector \(\begin{pmatrix}5\\-12\end{pmatrix}\).
Find the velocity vector of \(P\).[2]
When \(t=0\), \(P\) passes through a point \(A\) which has position vector \(\begin{pmatrix}3\\6\end{pmatrix}\).
Write down the position vector of \(P\) at time \(t\).[2]
At the same time that \(P\) passes through \(A\), a particle \(Q\) passes through a point \(B\).
The position vector of \(Q\) at time \(t\) is given by \(\begin{pmatrix}8t-5\\2-25t\end{pmatrix}\).
The distance between \(P\) and \(Q\) at time \(t\) is \(d\).
Show that \(d^2=mt^2+nt+r\), where \(m,n\) and \(r\) are integers to be found.[3]
Hence show that \(P\) and \(Q\) do not collide.[1]