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Q.
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
Vector Algebra
Solution:
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 $=2$