The volume of parallelopiped, whose coterminous edges are given by $\bar{u}=\hat{i}+\hat{j}+\lambda \hat{k}$, $\bar{v}=\hat{i}+\hat{j}+3 \hat{k}, \bar{w}=2 \hat{i}+\hat{j}+\hat{k}$ is 1 cu. units. If $ heta$ is the angle between $\bar{u}$ and $\bar{w}$, then the value of $\cos heta$ is

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The volume of parallelopiped, whose coterminous edges are given by $\bar{u}=\hat{i}+\hat{j}+\lambda \hat{k}$, $\bar{v}=\hat{i}+\hat{j}+3 \hat{k}, \bar{w}=2 \hat{i}+\hat{j}+\hat{k}$ is 1 cu. units. If $	heta$ is the angle between $\bar{u}$ and $\bar{w}$, then the value of $\cos 	heta$ is

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$\begin{aligned} & 	ext { Volume of parallelepiped }=\left[\begin{array}{lll}\overrightarrow{\mathrm{u}} & \overrightarrow{\mathrm{v}} & \overrightarrow{\mathrm{w}}\end{array}ight] \ & \quad\left|\begin{array}{lll}1 & 1 & \lambda \ 1 & 1 & 3 \ 2 & 1 & 1\end{array}ight|=1 \ & \Rightarrow \lambda=2 \ & 	herefore \quad \cos 	heta=\frac{2+1+2}{\sqrt{6} \cdot \sqrt{6}}=\frac{5}{6}\end{aligned}$

The volume of parallelopiped, whose coterminous edges are given by $\bar{u}=\hat{i}+\hat{j}+\lambda \hat{k}$…

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