Mixed practice: parallel vectors, unit vectors, displacement, distance and parameters Problem set A Answers

1. (a) \(p=-3,\ q=9\)
2. (b) \(p=2,\ q=6\)

1. (a) \(\begin{pmatrix}- \frac{4}{9} \\ \frac{4}{9} \\ \frac{7}{9}\end{pmatrix}\)
2. (b) \(\begin{pmatrix}\frac{40}{3} \\ \frac{40}{3} \\ - \frac{20}{3}\end{pmatrix}\)

1. (a) \(\begin{pmatrix}2 \\ 3 \\ -3\end{pmatrix}\)
2. (b) \(\begin{pmatrix}-5 \\ 5 \\ 4\end{pmatrix}\)
3. (c) \(\begin{pmatrix}7 \\ -2 \\ -7\end{pmatrix}\)

1. (a) \(\sqrt{34}\)
2. (b) \(10\)

\(x=-1,\ y=2,\ z=7\)

1. (a) \(\begin{pmatrix}1 \\ -10 \\ 19\end{pmatrix}\)
2. (b) \(3 \sqrt{13}\)

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

\(t=-2\ \text{or}\ t=1\)

\(10.5\) N

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

1. (a) \(\mathbf{b}-\mathbf{a}\)
2. (b) \(\frac{3}{5}\mathbf{a}+\frac{2}{5}\mathbf{b}\)
3. (c) \(\frac{3}{5}\mathbf{a}- \frac{1}{10}\mathbf{b}\)

1. (a) \(p=-2\)
2. (b) \(\lambda=2,\ k=11\)

1. (a) \(\lambda=-1.10\text{ or }\lambda=2.21\)
2. (b) \(t=-2.58\text{ or }t=0.581\)
3. (c) \(2.89\)

1. (a) \(\mathbf{i}+2\mathbf{j}+4\mathbf{k}\)
2. (b) \(R(-5, 8, 0)\)