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Question Number 118083 by pramod1977 last updated on 15/Oct/20

Answered by bemath last updated on 15/Oct/20

$$\mathrm{let}\overrightarrow{\mathrm{a}}=(2,1,-2)=\mathrm{diagonal}\mathrm{and}\overrightarrow{\mathrm{b}}=(3,1,-1)=\mathrm{side}$$$$\mathrm{The}\mathrm{area}\mathrm{of}\mathrm{parallelogram}=\mid \overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}\mid$$$$\mathrm{where}\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}=\left|\begin{array}{c}21-2\\ 31-1\end{array}\right|$$$$\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}}=i-4j-k$$$$\mathrm{The}\mathrm{area}=\sqrt{1+16+1}=3\sqrt{2}\mathrm{sq}\mathrm{units}$$

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