Given two vectors $\mathbf{a}=2\mathbf{i}+\mathbf{j}-2\mathbf{k}$ and \(\mathbf{b}=3\mathbf{i}+4\m

Question

Given two vectors $\mathbf{a}=2\mathbf{i}+\mathbf{j}-2\mathbf{k}$ and $\mathbf{b}=3\mathbf{i}+4\mathbf{j}-\mathbf{k}$, find: a unit vector perpendicular to both $\mathbf{a}$ and $\mathbf{b}$. the exact value of $\sin\theta$, where $\theta$ is the angle between $\mathbf{a}$ and $\mathbf{b}$.

Accepted Answer

(i) $\dfrac1{3\sqrt{10}}\begin{pmatrix}7\-4\5\end{pmatrix}$ (ii) $\sqrt{\dfrac5{13}}$

Vectors - Angles Between Vectors

Vectors - Angles Between Vectors

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