Question

Find the angle between $\frac{x}{-1}=\frac{y-2}{2}=\frac{z-3}{6}$ and $\frac{x+1}{6}=\frac{y+2}{2}=\frac{z-1}{3}$

Answer 1

Abgle between lines $\frac{x}{-1}=\frac{y-2}{2}=\frac{Z-3}{6}$ and $\frac{x+1}{6}=\frac{y+2}{2}=\frac{z-1}{3}$

$\because Cos\theta =\frac{-1\times 6+2\times 2+6\times 3}{\sqrt{(-1{)}^2+(2{)}^2+(6{)}^2}\sqrt{(6{)}^2+(2{)}^2+(3{)}^2}}$

$\Rightarrow cos\theta =\frac{16}{\sqrt{41}\sqrt{49}}$

$\Rightarrow \theta =co{s}^{-1}\left[\frac{16}{7\sqrt{41}}\right]$