Magnitude of a vector and unit vectors Problem set B Answers

1. (a) \(11\)
2. (b) \(\sqrt{69}\)

\(13\)

\(\begin{pmatrix}- \frac{6}{7} \\ \frac{2}{7} \\ \frac{3}{7}\end{pmatrix}\text{ and }\begin{pmatrix}\frac{6}{7} \\ - \frac{2}{7} \\ - \frac{3}{7}\end{pmatrix}\)

1. (a) \(\frac{6}{11}\mathbf{i}- \frac{7}{11}\mathbf{j}+\frac{6}{11}\mathbf{k}\)
2. (b) \(\frac{1}{\sqrt{10}}(3\mathbf{i}+\mathbf{j})\)

\(\begin{pmatrix}6 \\ 9 \\ 18\end{pmatrix}\)

\(\begin{pmatrix}3 \sqrt{6} \\ - 6 \sqrt{6} \\ 3 \sqrt{6}\end{pmatrix}\)

\(18.8\) m

\(k=\pm\frac{1}{7}\)

\(\begin{pmatrix}\frac{16 \sqrt{5}}{5} \\ 0 \\ - \frac{8 \sqrt{5}}{5}\end{pmatrix}\text{ and }\begin{pmatrix}- \frac{16 \sqrt{5}}{5} \\ 0 \\ \frac{8 \sqrt{5}}{5}\end{pmatrix}\)