Given two vectors $\mathbf{a}=2\mathbf{i}+\mathbf{j}-2\mathbf{k}$ and $\mathbf{b}=\mathbf{j}+3\mathb

Question

Given two vectors $\mathbf{a}=2\mathbf{i}+\mathbf{j}-2\mathbf{k}$ and $\mathbf{b}=\mathbf{j}+3\mathbf{k}$, find: a unit vector perpendicular to both $\mathbf{a}$ and $\mathbf{b}$. the exact value of $\sin 	heta $, where $	heta $ is the angle between $\mathbf{a}$ and $\mathbf{b}$.

Accepted Answer

(i) $\displaystyle\frac{1}{\sqrt{90}} \begin{pmatrix} 7 \\ -4 \\ 5 \end{pmatrix}$; (ii) $\sin\theta = \sqrt{\displaystyle\frac{5}{13}}$

Unit 13.1 Worked Example 4

Unit 13.1 Worked Example 4

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