Scalar multiplication and parallel vectors Problem set A Answers

1. (a) \(\begin{pmatrix}16\\-7\\8\end{pmatrix}\)
2. (b) \(\begin{pmatrix}-11\\-9\\14\end{pmatrix}\)

1. (a) \(\begin{pmatrix}-5\\-7\end{pmatrix}\)
2. (b) \(\begin{pmatrix}10\\17\end{pmatrix}\)

\(p=-20,\ q=12\)

\(p=-4,\ q=-14\)

1. (a) \(\frac{1}{2}\mathbf{b}\)
2. (b) \(3\mathbf{b}\)
3. (c) \(\mathbf{a}+\frac{5}{2}\mathbf{b}\)

1. (a) \(\frac{1}{2}\mathbf{a}\)
2. (b) \(-\mathbf{a}+\mathbf{b}\)
3. (c) \(-\frac{3}{2}\mathbf{a}+\mathbf{b}\)

1. (a) \(\begin{pmatrix}13\\-16\\0\end{pmatrix}\)
2. (b) \(p=4,\ q=-6\)

\(k=6\) or \(k=-6\)

\(\mathbf{n}=-\frac{2}{3}\mathbf{m}\), so they are parallel and point opposite ways