Question

The angle between the lines $2x=3y=-z$ and $6x=-y=-4z$ is

• A. $0^{\circ }$
• B. ${45}^{\circ }$
• C. ${90}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is C ${90}^{\circ }$

The direction ratios of $2x=3y=-z\Rightarrow \frac{x}{3}=\frac{y}{2}=\frac{z}{-6}$ are $3,2,-6$ and direction ratios of $6x=-y=-4z\Rightarrow \frac{x}{2}=\frac{y}{-12}=\frac{z}{-3}$ are $2,-12,-3$.
Therefore, angle $\theta$ between the lines is given by
$\cos \theta =\left|\frac{3\left(2\right)+2(-12)+(-6)(-3)}{\sqrt{(3{)}^2+(2{)}^2+(-6{)}^2}\sqrt{(2{)}^2+(-12{)}^2+(-3{)}^2}}\right|$

$\Rightarrow \cos \theta =0\Rightarrow \theta =\frac{\pi }{2}$