Question

The plane $x-2y+z-6=0$ and the line $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ are related as.

• A. Parallel to the plane
• B. At right angle to the plane
• C. Lies in the plane
• D. Meets the plane obliquely

Answer 1

Answer: (A)

Parallel to the plane

Given line is $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ any point on the line is $(t,2t,3t)$. It lies in the given plane, if $t-2\left(2t\right)+3t-6=0$
i.e., $0\cdot t=6$, which is not true for any real $t$. So, the line and plane do not meet. i.e., the line is parallel to the plane.