Scalar multiplication and parallel vectors Problem set B Answers

1. (a) \(\begin{pmatrix}-3\\-21\\36\end{pmatrix}\)
2. (b) \(\begin{pmatrix}-16\\26\\-15\end{pmatrix}\)

1. (a) \(\begin{pmatrix}22\\3\end{pmatrix}\)
2. (b) \(\begin{pmatrix}8\\-31\end{pmatrix}\)

\(p=-20,\ q=45\)

\(p=-6,\ q=-15\)

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

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

1. (a) \(\begin{pmatrix}10\\-21\\25\end{pmatrix}\)
2. (b) \(p=-12,\ q=18\)

\(k=10\) or \(k=-10\)

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