Magnitude of a vector and unit vectors Problem set A Answers

1. (a) \(7\)
2. (b) \(\sqrt{35}\)

\(9\)

\(\begin{pmatrix}\frac{1}{3} \\ - \frac{2}{3} \\ \frac{2}{3}\end{pmatrix}\text{ and }\begin{pmatrix}- \frac{1}{3} \\ \frac{2}{3} \\ - \frac{2}{3}\end{pmatrix}\)

1. (a) \(\frac{4}{9}\mathbf{i}+\frac{1}{9}\mathbf{j}+\frac{8}{9}\mathbf{k}\)
2. (b) \(\frac{1}{\sqrt{5}}(\mathbf{i}-2\mathbf{j})\)

\(\begin{pmatrix}2 \\ 8 \\ 16\end{pmatrix}\)

\(\begin{pmatrix}4 \sqrt{3} \\ 4 \sqrt{3} \\ - 4 \sqrt{3}\end{pmatrix}\)

\(23.9\) m

\(k=\pm\frac{1}{3}\)

\(\begin{pmatrix}\frac{5 \sqrt{14}}{7} \\ - \frac{10 \sqrt{14}}{7} \\ \frac{15 \sqrt{14}}{7}\end{pmatrix}\text{ and }\begin{pmatrix}- \frac{5 \sqrt{14}}{7} \\ \frac{10 \sqrt{14}}{7} \\ - \frac{15 \sqrt{14}}{7}\end{pmatrix}\)