9709 P31 - Jun 2026 - Q9 - 7 marks
9101
Points \(A\) and \(B\) have position vectors \(\begin{pmatrix}2\\-5\\3\end{pmatrix}\) and \(\begin{pmatrix}-6\\4\\1\end{pmatrix}\), respectively. The line \(t\) passes through \(A\) and \(B\).
(a) Find a vector equation for \(t\). [2]
The line \(s\) has equation \(\mathbf r=\begin{pmatrix}1\\3\\4\end{pmatrix}+\mu\begin{pmatrix}-1\\2\\-1\end{pmatrix}\).
(b) Determine whether \(s\) and \(t\) are parallel, intersect or are skew. [5]
