Questions: 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. \(\quad \mathbf{e} = \begin{bmatrix}2\\-1\\4\end{bmatrix}\)
1.6. \(\quad \mathbf{f} = \begin{bmatrix}-3\\6\\2\end{bmatrix}\)
1.7. \(\quad \mathbf{g} = \begin{bmatrix}5\\1\\\sqrt{2}\end{bmatrix}\)
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. \(\quad \mathbf{q} = \begin{bmatrix}5\\-2\\14\end{bmatrix}\)
1.13. \(\quad \mathbf{u} = \begin{bmatrix}7\\2\\-1\end{bmatrix}\)
1.14. \(\quad \mathbf{v} = \begin{bmatrix}12\\9\\8\end{bmatrix}\)
Q2
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. \(\quad \mathbf{e} = \begin{bmatrix}3\\0\\2\end{bmatrix}\)
2.6. \(\quad \mathbf{f} = \begin{bmatrix}-3\\1\\7\end{bmatrix}\)
2.7. \(\quad \mathbf{g} = \begin{bmatrix}-5\\0\\\sqrt{2}\end{bmatrix}\)
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. \(\quad \mathbf{q} = \begin{bmatrix}4\\-3\\12\end{bmatrix}\)
2.13. \(\quad \mathbf{u} = \begin{bmatrix}6\\5\\4\end{bmatrix}\)
2.14. \(\quad \mathbf{v} = \begin{bmatrix}2\\4\\8\end{bmatrix}\)
After attempting the questions above, please click this link to find the answers.
Version history and licensing
v1.0: initial version created 08/23 by Zheng Chen as part of a University of St Andrews STEP project.
- v1.1: edited 05/24 by tdhc.