Column vectors and base vectors i, j, k Problem set B Answers

1. (a) \(\mathbf{p}=\begin{pmatrix}5\\2\end{pmatrix}\)
2. (b) \(\mathbf{q}=\begin{pmatrix}1\\-4\end{pmatrix}\)

1. (a) \(\mathbf{r}=\begin{pmatrix}-5\\3\end{pmatrix}\)
2. (b) \(\mathbf{s}=\begin{pmatrix}-2\\-4\end{pmatrix}\)

1. (a) \(-6\mathbf{i}+5\mathbf{j}\)
2. (b) \(4\mathbf{i}-2\mathbf{j}\)

1. (a) \(\begin{pmatrix}2\\-5\\1\end{pmatrix}\)
2. (b) \(\begin{pmatrix}0\\4\\-9\end{pmatrix}\)
3. (c) \(\begin{pmatrix}-5\\0\\6\end{pmatrix}\)

1. (a) \(\begin{pmatrix}-9\\4\end{pmatrix}\)
2. (b) \(-9\mathbf{i}+4\mathbf{j}\)

1. (a) \(\begin{pmatrix}40\\-25\\-12\end{pmatrix}\)
2. (b) \(40\mathbf{i}-25\mathbf{j}-12\mathbf{k}\)
3. (c) Vector

\(p=-3,\ q=-1\)

\(\mathbf{v}=\begin{pmatrix}5\\-3\end{pmatrix}=5\mathbf{i}-3\mathbf{j}\)