Question

The distance of the point $P(2,-3,4)$ from the plane $r\cdot (\hat{i}+\hat{j}+\hat{k})=5$ measured parallel to $z$-axis, is

• A. 1
• B. $\sqrt{2}$
• C. 2
• D. 4

Answer 1

Answer: (C)

Equation of plane is $x+y+z=5$
Straight line passing through $(2,-3,4)$ and parallel to $z$-axis
$\frac{x-2}{0}=\frac{y+3}{0}=\frac{z-4}{1}=r$
a point on the line is $(2,-3,r+4)$
which lies on the plane $x+y+z=5$
$\therefore 2-3+r+4=5\Rightarrow r=2$
Hence, required distance is $=2$