Calculating Unknown Variables in Parallel Vector Systems
Calculating Unknown Variables in Parallel Vector Systems
TGM Original
Given that \(\mathbf{p} = \begin{pmatrix} 1 \\ -4 \end{pmatrix}\), \(\mathbf{q} = \begin{pmatrix} -3 \\ -4 \end{pmatrix}\) and \(\mathbf{r} = \begin{pmatrix} m \\ -2 \end{pmatrix}\).
- Find \(|\mathbf{q}|\).
- Express \(2\mathbf{p} - \mathbf{q}\) as a column vector.
- Given that \(\mathbf{p}\) is parallel to \(\mathbf{r}\), find \(m\).
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Answer:(a) \(5\) (b) \(\begin{pmatrix}5\\-4\end{pmatrix}\) (c) \(\dfrac12\)
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