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Solve this following

Question:

Let the volume of a parallelopiped whose coterminous edges are given by $\overrightarrow{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}, \overrightarrow{\mathrm{v}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{w}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ be $1 \mathrm{cu}$. unit. If $\theta$ be the angle between the edges $\overrightarrow{\mathrm{u}}$ and $\overrightarrow{\mathrm{w}}$, then $\cos \theta$ can be

  1. $\frac{7}{6 \sqrt{3}}$

  2. $\frac{5}{7}$

  3. $\frac{7}{6 \sqrt{6}}$

  4. $\frac{5}{3 \sqrt{3}}$


Correct Option: 1

Solution:

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