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)

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