Question

Find the angle between the lines $\frac{x-2}{3}=\frac{y+1}{-2}$ , $z=2$ and $\frac{x-1}{1}=\frac{2y+3}{3}$ , $\frac{z+5}{2}$.

Answer 1

The given lines have been mapped as per the image,

It is known that:

$cos\theta =\frac{\overrightarrow{a}.\overrightarrow{b}}{\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|}$

$\Rightarrow cos\theta =\frac{(3i-2j).(i+\frac{3j}{2}+2k)}{|3i-2j||i+\frac{3j}{2}+2k|}$

$\Rightarrow cos\theta =3-3$

$\Rightarrow cos\theta =0$

$\Rightarrow \theta ={90}^o$

Hence the angle between the lines is ${90}^o$