The angle between the two lines $\frac{x-4}{1}=\frac{y+4}{2}=\frac{z+1}{2}$ and…

The angle between the two lines $\frac{x-4}{1}=\frac{y+4}{2}=\frac{z+1}{2}$ and $\frac{x+1}{2}=\frac{y+3}{2}=\frac{z-4}{-1}$ is
  1. $\cos ^{-1}\left(\frac{4}{9}\right)$
  2. $\cos ^{-1}\left(\frac{5}{9}\right)$
  3. $\cos ^{-1}\left(\frac{1}{9}\right)$
  4. $\cos ^{-1}\left(\frac{2}{9}\right)$

Solution

Let $\theta$ be the required angle $\begin{array}{l} \cos \theta=\left|\frac{1(2)+2(2)+2(-1)}{\sqrt{1+4+4} \sqrt{4+4+1}}\right|=\frac{|2+4-2|}{3 \times 3} \\ \cos \theta=\frac{4}{9} \quad \Rightarrow \theta=\cos ^{-1}\left(\frac{4}{9}\right) \end{array}$

Asked in: MHT CET 2020 (15 Oct Shift 2)

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