Q.The angle between the line $\vec{r} = \hat{i} + 2\hat{j} + \hat{k} + \lambda (3\hat{i} + \hat{j} + 2\hat{k})$ and the plane $\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 8$ is

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

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

\sin^{-1}(7/3\sqrt{14})

\cos^{-1}(7/3\sqrt{14})

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(3i^+j^+2k^)\vec{r} = \hat{i} + 2\hat{j} + \hat{k} + \lambda (3\hat{i} + \hat{j} + 2\hat{k})r=i^+2j^​+k^+λ(3i^+j^​+2k^) and the plane r⃗⋅(i^+j^+k^)=8\vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 8r⋅(i^+j^​+k^)=8 is