If the volume of the parallelopiped is $158 \mathrm{cu}$. units whose coterminus edges are given by the vectors $\bar{a}=(\hat{i}+\hat{j}+n \hat{k}), \bar{b}=2 \hat{i}+4 \hat{j}-n \hat{k}$ and $\bar{c}=\hat{i}+n \hat{j}+3 \hat{k}$, where $n \geq 0$, then the value of $n$ is

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Volume of parallelopiped }=\left|\begin{array}{ccc}1 & 1 & n \ 2 & 4 & -n \ 1 & n & 3\end{array}ight|=158 \ & \Rightarrow 1\left(12+n^2ight)-1(6+n)+n(2 n-4)-158 \ & \Rightarrow 3 n^2-5 n-152=0 \ & \Rightarrow(3 n+19)(n-8)=0 \ & \Rightarrow n=8\end{aligned}$

If the volume of the parallelopiped is $158 \mathrm{cu}$. units whose coterminus edges are given by the…

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