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

1. (a) \(p=-12,\ q=-4\)
2. (b) \(p=12,\ q=-3\)

1. (a) \(\begin{pmatrix}\frac{2}{7} \\ - \frac{3}{7} \\ \frac{6}{7}\end{pmatrix}\)
2. (b) \(\begin{pmatrix}\frac{20}{3} \\ - \frac{20}{3} \\ \frac{35}{3}\end{pmatrix}\)

1. (a) \(\begin{pmatrix}3 \\ -9 \\ 3\end{pmatrix}\)
2. (b) \(\begin{pmatrix}5 \\ -4 \\ -8\end{pmatrix}\)
3. (c) \(\begin{pmatrix}-2 \\ -5 \\ 11\end{pmatrix}\)

1. (a) \(2 \sqrt{6}\)
2. (b) \(13\)

\(x=1,\ y=3,\ z=5\)

1. (a) \(\begin{pmatrix}1 \\ 16 \\ 1\end{pmatrix}\)
2. (b) \(\sqrt{317}\)

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

\(t=-2\ \text{or}\ t=5\)

\(4.47\) kN

1. (a) \(\mathbf{a}+\frac{1}{2}\mathbf{b}\)
2. (b) \(- \frac{1}{2}\mathbf{a}+\frac{1}{2}\mathbf{b}\)
3. (c) \(\frac{3}{4}\mathbf{a}-\mathbf{b}\)

1. (a) \(\mathbf{a}-\mathbf{b}\)
2. (b) \(\frac{1}{4}\mathbf{a}+\frac{3}{4}\mathbf{b}\)
3. (c) \(- \frac{1}{4}\mathbf{a}+\frac{3}{4}\mathbf{b}\)

1. (a) \(p=3\)
2. (b) \(\lambda=4,\ k=5\)

1. (a) \(\lambda=-0.964\text{ or }\lambda=1.51\)
2. (b) \(t=-1.39\text{ or }t=1.84\)
3. (c) \(3.24\)

1. (a) \(2\mathbf{i}-\mathbf{j}+2\mathbf{k}\)
2. (b) \(R(12, -7, -4)\)