Question

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

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

Answer 1

The correct option is A ${90}^0$

From given line
$\frac{x}{3}=\frac{y}{2}=\frac{z}{-6}$ and $\frac{x}{2}=\frac{y}{-12}=\frac{z}{-3}$

$\Rightarrow \cos \theta =\frac{a_1{a}_2+b_1{b}_2+c_1{c}_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}}$

$\Rightarrow \cos \theta =\frac{6-24+18}{\sqrt{3^2+2^2+{(-6)}^2}\sqrt{2^2+{(-12)}^2+{(-3)}^2}}=0$

$\Rightarrow \theta ={90}^0$