0606 P12 - Nov 2022 - Q5 - 8 marks
7864
(a) Find the vector with magnitude \(200\) in the direction of
\(\begin{pmatrix}7\\-24\end{pmatrix}.\)
(b) The diagram shows triangle \(AOB\) such that \(\overrightarrow{OA}=\mathbf a\), and \(\overrightarrow{OB}=\mathbf b\). The point \(C\) lies on the line \(AB\) such that \(AC:AB=1:3\). Find the vector \(\overrightarrow{OC}\) in terms of \(\mathbf a\) and \(\mathbf b\), giving your answer in its simplest form.
(c) Given the vector equation
\(p\begin{pmatrix}2\\1\end{pmatrix}+q\begin{pmatrix}2\\4\end{pmatrix} =5\begin{pmatrix}-p+1\\p+q\end{pmatrix},\)
find the values of \(p\) and \(q\).
