The angle between the lines \(\displaystyle\frac{x-3}{1}=\frac{y+2}{2}=\frac{z-1}{-1}\) and \(\displaystyle\frac{x+1}{2}=\frac{y}{1}=\frac{z-4}{1}\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{\pi}{3}\)
The direction ratios are 1, 2, −1 and 2, 1, 1. The angle between two lines is given by
\( \displaystyle \cos\theta = \frac{|a_1a_2+b_1b_2+c_1c_2|}{\sqrt{a_1^2+b_1^2+c_1^2}\,\sqrt{a_2^2+b_2^2+c_2^2}} \)
\((1)(2)+(2)(1)+(-1)(1) = 3\)
\(\sqrt{1+4+1} = \sqrt{6}\) and \(\sqrt{4+1+1} = \sqrt{6}\)
\( \displaystyle \cos\theta = \frac{3}{\sqrt{6}\,\sqrt{6}} = \frac{1}{2} \)
\( \displaystyle \theta = \frac{\pi}{3} \)