Question

Let $\pi_1$ denotes the equation of the plane to which the vector $\langle 1,1,0\rangle$ is normal and which contains the line $L$ whose equation is $r=\hat{i}+\hat{j}+\hat{k}+\lambda(\hat{i}-\hat{j}-\hat{k}) \cdot \pi_2$ denotes the equation of the plane containing the line $L$ and a point with position vector $\langle 0,1,0\rangle$.
The acute angle between $\pi_1$ and $\pi_2$, is

• A. $\tan ^{-1} 1-\tan ^{-1}(\sqrt{2}-1)$
• B. $\tan ^{-1} 1-\tan ^{-1}(2-\sqrt{3})$
• C. $\tan ^{-1} 1-\tan ^{-1}(\sqrt{2}+1)$
• D. $\tan ^{-1} 1-\tan ^{-1}(2+\sqrt{3})$

Answer 1

Answer: (B)

Correct answer is (b) $\tan ^{-1} 1-\tan ^{-1}(2-\sqrt{3})$