Q.The angle between the line $\vec{r} = (\hat{i} + 2\hat{j} - \hat{k}) + \lambda (\hat{i} - \hat{j} + \hat{k})$ and the plane $\vec{r} \cdot (2\hat{i} - \hat{j} + \hat{k}) = 4$ is

\sin^{-1}(1/3)

\cos^{-1}(1/3)

\sin^{-1}(\sqrt{2}/3)

\cos^{-1}(\sqrt{2}/3)

The correct solution involves applying the fundamental concept to derive the final value step by step...

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Q.The angle between the line r⃗=(i^+2j^−k^)+λ(i^−j^+k^)\vec{r} = (\hat{i} + 2\hat{j} - \hat{k}) + \lambda (\hat{i} - \hat{j} + \hat{k})r=(i^+2j^​−k^)+λ(i^−j^​+k^) and the plane r⃗⋅(2i^−j^+k^)=4\vec{r} \cdot (2\hat{i} - \hat{j} + \hat{k}) = 4r⋅(2i^−j^​+k^)=4 is