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Unknown components from lengths

Unknown components from lengths

Secondary 4
4 marks
  1. The column vector \(\mathbf{p}=\begin{pmatrix}-2\\ k\end{pmatrix}\) has length \(\sqrt{29}\). Work out both values of \(k\).[2]
  2. The column vector \(\mathbf{q}=\begin{pmatrix}0\\ h\end{pmatrix}\) has length 6. Work out both values of \(h\), and say which way \(\mathbf{q}\) points for each.[2]

Solution:

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Answer:(a) \(k=5\) or \(k=-5\) (b) \(h=6\) (vertically up) or \(h=-6\) (vertically down)

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