Question

A line with positive direction cosines passes through the point $P(2,-1,2)$ and makes equal angles with the coordinate axes. The line meets the plane $2x+y+z=9$ at point $Q$. The length of the line segment $PQ$ equals

• A. 1
• B. $\sqrt{2}$
• C. $\sqrt{3}$
• D. 2

Answer 1

The correct option is C $\sqrt{3}$

$D.C$ of the line are $\frac{1}{\sqrt{3}}$ , $\frac{1}{\sqrt{3}}$ , $\frac{1}{\sqrt{3}}$

Any point on the line at a distance $t$ from $P(2,-1,2)$ is $(2+\frac{t}{\sqrt{3}},-1+\frac{t}{\sqrt{3}},2+\frac{t}{\sqrt{3}})$

which lies on $2x+y+z=9$.

$\Rightarrow t=\sqrt{3}$