Question

Let ${\pi }_1$ denotes the equation of the plane to which the vector $⟨1,1,0⟩$ 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 $⟨0,1,0⟩$.
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) ${\tan }^{-1}1-{\tan }^{-1}(2-\sqrt{3})$