Questions: Introduction to vectors

Author

Zheng Chen

Summary

A selection of questions for the study guide on introduction to vectors.

Before attempting these questions, it is recommended that you read Guide: Introduction to vectors.

Q1

Find the magnitude of the following vectors.

1.1. \(\quad \mathbf{a} = -\mathbf{i} + 3\mathbf{j}\)

1.2. \(\quad \mathbf{b} = 2\mathbf{i}+4\mathbf{j}+6\mathbf{k}\)

1.3. \(\quad \mathbf{c} = \mathbf{i}-\mathbf{j}+4\mathbf{k}\)

1.4. \(\quad \mathbf{d} = 5\mathbf{i}-2\mathbf{j}+\mathbf{k}\)

1.5. \(\quad \mathbf{e} = \begin{pmatrix}2\\-1\\4\end{pmatrix}\)

1.6. \(\quad \mathbf{f} = \begin{pmatrix}-3\\6\\2\end{pmatrix}\)

1.7. \(\quad \mathbf{g} = \begin{pmatrix}5\\1\\\sqrt{2}\end{pmatrix}\)

1.8. \(\quad \mathbf{h} = 6\mathbf{i}+2\mathbf{j}+2\mathbf{k}\)

1.9. \(\quad \mathbf{m} = -3\mathbf{i}+3\mathbf{j}-3\mathbf{k}\)

1.10. \(\quad \mathbf{n} = 2\mathbf{i}+4\mathbf{j}+4\mathbf{k}\)

1.11. \(\quad \mathbf{p} = 8\mathbf{i}-2\mathbf{j}+16\mathbf{k}\)

1.12. \(\quad \mathbf{q} = \begin{pmatrix}5\\-2\\14\end{pmatrix}\)

1.13. \(\quad \mathbf{u} = \begin{pmatrix}7\\2\\-1\end{pmatrix}\)

1.14. \(\quad \mathbf{v} = \begin{pmatrix}12\\9\\8\end{pmatrix}\)

Find the unit vectors in the directions of the following vectors.

2.1. \(\quad \mathbf{a} = -2\mathbf{i} + 3\mathbf{j}\)

2.2. \(\quad \mathbf{b} = -2\mathbf{i}+4\mathbf{j}-6\mathbf{k}\)

2.3. \(\quad \mathbf{c} = \mathbf{i}+2\mathbf{j}+4\mathbf{k}\)

2.4. \(\quad \mathbf{d} = 4\mathbf{i}-2\mathbf{j}+3\mathbf{k}\)

2.5. \(\quad \mathbf{e} = \begin{pmatrix}3\\0\\2\end{pmatrix}\)

2.6. \(\quad \mathbf{f} = \begin{pmatrix}-3\\1\\7\end{pmatrix}\)

2.7. \(\quad \mathbf{g} = \begin{pmatrix}-5\\0\\\sqrt{2}\end{pmatrix}\)

2.8. \(\quad \mathbf{h} = -3\mathbf{i}+1\mathbf{j}+1\mathbf{k}\)

2.9. \(\quad \mathbf{m} = -3\mathbf{i}+3\mathbf{j}-3\mathbf{k}\)

2.10. \(\quad \mathbf{n} = 3\mathbf{i}+6\mathbf{j}+9\mathbf{k}\)

2.11. \(\quad \mathbf{p} = 3\mathbf{i}-4\mathbf{j}-5\mathbf{k}\)

2.12. \(\quad \mathbf{q} = \begin{pmatrix}4\\-3\\12\end{pmatrix}\)

2.13. \(\quad \mathbf{u} = \begin{pmatrix}6\\5\\4\end{pmatrix}\)

2.14. \(\quad \mathbf{v} = \begin{pmatrix}2\\4\\8\end{pmatrix}\)

v1.0: initial version created 08/23 by Zheng Chen as part of a University of St Andrews STEP project.