Unknowns in a combination of vectors

Unknowns in a combination of vectors

Secondary 4
4 marks

It is given that \(\mathbf{p}=\begin{pmatrix}x\\ 2x\end{pmatrix}\), \(\mathbf{q}=\begin{pmatrix}3\\ y\end{pmatrix}\) and \(3\mathbf{p}-\mathbf{q}=\begin{pmatrix}9\\ 17\end{pmatrix}\).

  1. Find the value of \(x\) and the value of \(y\).[2]
  2. Find \(|\mathbf{p}|\), leaving your answer in surd form.[2]

Solution:

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Answer:(a) \(x=4\), \(y=7\) (b) \(4\sqrt5\)

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