Question

The distance of the point $(1,-2,3)$ from the plane $x-y+z=5$ measured parallel to a line, whose direction ratios are $2,3,-6$ is

• A. $2$
• B. $5$
• C. $3$
• D. $1$

Answer 1

The correct option is D $1$

Equation of line through point $(1,-2,3)$ and parallel
to line with direction ratios $2,3,-6$ is
$L:\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-3}{-6}=\lambda$ (say)
Any point on line $L$ is $P(2\lambda +1,3\lambda -2,-6\lambda +3)$
Since $P$ lies on plane, $x-y+z=5$
$\therefore$ $2\lambda +1-3\lambda +2-6\lambda +3=5$
$\Rightarrow \lambda =\frac{1}{7}$
$\therefore$ Required distance
$=\sqrt{(2\lambda {)}^2+(3\lambda {)}^2+(6\lambda {)}^2}$
$=7\lambda$
$=1$ unit