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Question Number 182176 by peter frank last updated on 05/Dec/22

Answered by MikeH last updated on 05/Dec/22

$$\mathrm{let}\overrightarrow{\mathrm{w}}=x\mathrm{i}+6\mathrm{j}+y\mathrm{k}$$$$\mathrm{orthogonal}\mathrm{to}\overrightarrow{\mathrm{u}}\mathrm{and}\overrightarrow{\mathrm{v}}\Rightarrow \overrightarrow{\mathrm{w}}=\overrightarrow{\mathrm{u}}\times \overrightarrow{\mathrm{v}}$$$$\Rightarrow x\mathrm{i}+6\mathrm{j}+y\mathrm{k}=\left|\begin{array}{ccc}\mathrm{i}& \mathrm{j}& \mathrm{k}\\ -1& 0& 1\\ -1& -2& 2\end{array}\right|$$$$\Rightarrow x\mathrm{i}+6\mathrm{j}+y\mathrm{k}=\mathrm{i}\left(2\right)-\mathrm{j}(-1)+\mathrm{k}\left(2\right)$$$$\Rightarrow x\mathrm{i}+6\mathrm{j}+y\mathrm{k}=2\mathrm{i}+\mathrm{j}+2\mathrm{k}$$$$x=2\mathrm{and}y=2$$$$\Rightarrow \overrightarrow{\mathrm{w}}=2\mathrm{i}+6\mathrm{j}+2\mathrm{k}$$

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