Question

Find the equation of the line through the origin which intersect the line $\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$ at an angle of $\frac{\pi }{2}$ and $\frac{x-3}{1}=\frac{y-3}{2}=\frac{z}{1}$ at an angle of $\frac{\pi }{2}$

Answer 1

Let $a,b,c$ be of required line

From $1st$ line $\Rightarrow 2a+b+c=0$ ------- $\left(1\right)$

From $2nd$ line $\Rightarrow a+2b+c=0$ ------- $\left(2\right)$

From $\left(1\right),\left(2\right)\Rightarrow a:b:c=1:1:3$

So the required line $\frac{x}{1}=\frac{y}{1}=\frac{z}{3}$