Question

Find the angle between the straight lines $\frac{x+1}{2}=\frac{y-2}{5}=\frac{z+3}{4}$ and
$\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{-3}$

• A. ${45}^o$
• B. ${30}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is D ${90}^o$

Given lines are $\frac{x+1}{2}=\frac{y-2}{5}=\frac{z+3}{4}$ and $\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{-3}$

The angle between the given lines is given by,
$\cos \theta =\frac{\left(2\right)\left(1\right)+\left(5\right)\left(2\right)+\left(4\right)(-3)}{\sqrt{4+25+16}\cdot \sqrt{1+4+9}}$

$=0$
Therefore, $\theta ={90}^o$