The volume of the tetrahedron having vertices $(1,-6,10)$, $(-1,-3,7),(5,-1, \lambda)$ and $(7,-4,7)$ is $11 \mathrm{cu}$. Units, then $\lambda=$

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Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Volume of a tetrahedron }=\frac{1}{6}\left|\begin{array}{lll}x_2-x_1 & y_2-y_1 & z_2-z_1 \ x_3-x_1 & y_3-y_1 & z_3-z_1 \ x_4-x_1 & y_4-y_1 & z_4-z_1\end{array}ight| \ & =\frac{1}{6}\left|\begin{array}{ccc}-2 & 3 & -3 \ 4 & 5 & \lambda-10 \ 6 & 2 & -3\end{array}ight| \ & \Rightarrow 11=\frac{1}{6}\{22 \lambda-88\} \Rightarrow \lambda=7\end{aligned}$

The volume of the tetrahedron having vertices $(1,-6,10)$, $(-1,-3,7),(5,-1, \lambda)$ and $(7,-4,7)$ is $11…

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