If $\mathrm{A}(1,-1,2), \mathrm{B}(5,7,-6), \mathrm{C}(3,4,-10)$ and $\mathrm{D}(-1,-4,-2)$ are the vertices of a quadrilateral $A B C D$, then its area is :

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{A}(1,-1,2) \ & \mathrm{B}(5,7,-6) \ & \mathrm{C}(3,4,-10) \ & \mathrm{D}(-1,-4,-2) \ & 	ext { Area }=\frac{1}{2}|\overrightarrow{\mathrm{AC}} 	imes \overrightarrow{\mathrm{BD}}|=\frac{1}{2}|(2 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}-12 \hat{\mathrm{k}}) 	imes(6 \hat{\mathrm{i}}+11 \hat{\mathrm{j}}-4 \hat{\mathrm{k}})| \ & =\frac{1}{2}|112 \hat{\mathrm{i}}-64 \hat{\mathrm{j}}-8 \hat{\mathrm{k}}| \ & =4|14 \hat{\mathrm{i}}-8 \hat{\mathrm{j}}-\hat{\mathrm{k}}| \ & =4 \sqrt{196+64+1} \ & =4 \sqrt{261} \ & =12 \sqrt{29}\end{aligned}$

If $\mathrm{A}(1,-1,2), \mathrm{B}(5,7,-6), \mathrm{C}(3,4,-10)$ and $\mathrm{D}(-1,-4,-2)$ are the vertices…

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