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Question id: 54. This question is similar to one that appeared in an IB Standard paper in 2014. The use of a calculator is allowed.

Consider two perpendicular vectors \(p\) and \(q\).

(a) Let \(r=p-q\). Draw a diagram to show what this relationship might look like.

(b) If \(p=\begin{pmatrix} 4 \\ 1 \\ -3 \\ \end{pmatrix}\) and \(q=\begin{pmatrix} 3 \\ n \\ -5 \\ \end{pmatrix}\), where \(n\in \mathbb Z\), find \(n\).

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