Question

The lines $2x=3y=-z$ and $6x=-y=-4z$

• A. Are perpendicular
• B. Are parallel
• C. Intersect at an angle ${45}^o$
• D. Intersect at an angle ${60}^o$

Answer 1

Answer: (A)

Are perpendicular

Here, Lines are $\frac{x}{\frac{1}{2}}=\frac{y}{\frac{1}{3}}=\frac{z}{-1}$ and $\frac{x}{\frac{1}{6}}=\frac{y}{-1}=\frac{z}{\frac{-1}{4}}$

Direction ratios of the lines are $<\frac{1}{2},\frac{1}{3},-1>$ and $<\frac{1}{6},-1,\frac{-1}{4}>$

Product of DR's i.e. $\frac{1}{2}\times \frac{1}{6}+\frac{1}{3}\times (-1)+(-1)\times \frac{-1}{4}=0$

Hence, both the lines are perpendicular,

Therefore, A is the correct option.