The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 \hat{i}-6 \hat{j}$ and $3 \hat{i}+4 \hat{j}-12 \hat{k}$, is

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Aicharya · Accepted Answer

Let $\overline{\mathrm{a}}=8 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}, \overline{\mathrm{b}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-12 \hat{\mathrm{k}}$ $\begin{aligned} & 	herefore \quad 	ext { Area of parallelogram }=\frac{1}{2}|\overline{\mathrm{a}} 	imes \overline{\mathrm{b}}| 	ext {. } \ & \overline{\mathrm{a}} 	imes \overline{\mathrm{b}}=\left|\begin{array}{ccc} \hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \ 8 & -6 & 0 \ 3 & 4 & -12 \end{array}ight|=72 \hat{\mathrm{i}}+96 \hat{\mathrm{j}}-50 \hat{\mathrm{k}} \ & 	herefore \quad \frac{1}{2}|\overrightarrow{\mathrm{a}} 	imes \overline{\mathrm{b}}|=\sqrt{5184+9216+2500} 	imes \frac{1}{2} \ & =\sqrt{16900} 	imes \frac{1}{2}=130 	imes \frac{1}{2}=65 \end{aligned}$

The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 \hat{i}-6 \hat{j}$ and…

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