Question

Foot of perpendicular drawn from the origin to the plane $2x-3y+4z=29$ is

• A. $(5,-1,4)$
• B. $(2,-3,4)$
• C. $(7,-1,3)$
• D. $(5,-2,3)$

Answer 1

Answer: (B)

Since, $PQ$ is perpendicular to the plane $2x-3y+4z=29.$
Hence, DR's of $PQ$ will be $<2,-3,4>$
Equation of line $PQ$ will be
$\frac{x-0}{2}=\frac{y-0}{-3}$
$=\frac{z-0}{4}=\lambda$ (say)
Coordinates of $Q$ will be $(2\lambda ,-3\lambda ,4\lambda )$
$\because Q$ lies on plane, so $4\lambda +9\lambda +16\lambda =29$
$\Rightarrow \lambda =1$
$\therefore$ Coordinates of $Q$ are $(2,-3,4)$