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

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

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

1. (a) \(7\mathbf{i}-2\mathbf{j}\)
2. (b) \(-3\mathbf{i}+5\mathbf{k}\)

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

1. (a) \(\begin{pmatrix}7\\-2\end{pmatrix}\)
2. (b) \(7\mathbf{i}-2\mathbf{j}\)

1. (a) \(\begin{pmatrix}-30\\20\\8\end{pmatrix}\)
2. (b) \(-30\mathbf{i}+20\mathbf{j}+8\mathbf{k}\)
3. (c) Scalar

\(p=2,\ q=-5\)

\(\mathbf{w}=\begin{pmatrix}-4\\5\end{pmatrix}=-4\mathbf{i}+5\mathbf{j}\)