Question

The angle between the pair of lines $\frac{x+3}{3}=\frac{y-1}{5}=\frac{z+3}{4}$ and $\frac{x+1}{1}=\frac{y-4}{4}=\frac{z-5}{2}$ is

• A. $\theta ={\cos }^{-1}\left[\frac{27}{5}\right]$
• B. $\theta ={\cos }^{-1}\left[\frac{19}{21}\right]$
• C. $\theta ={\cos }^{-1}\left[\frac{8\sqrt{3}}{15}\right]$
• D. $\theta ={\cos }^{-1}\left[\frac{5\sqrt{3}}{16}\right]$

Answer 1

Answer: (A), (B), (C), (D)

$\cos \theta =\frac{3\times 1+5\times 4+4\times 2}{\sqrt{3^2+5^2+4^2}\times \sqrt{1^2+4^2+2^2}}=\frac{31}{5\sqrt{42}}$
$\theta ={\cos }^{-1}\frac{31}{5\sqrt{42}}$