Question

Foot of the 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

The correct option is B $(2,-3,4)$

Let the coordinate of the foot of the perpendicular is $(x,y,z)$ then DC's of the line joining the origin and $(x,y,z)$ is $(x,y,z)$
$\because \text{the line is perpendicular to the given plane}\therefore x=2\lambda ,y=-3\lambda ,z=4\lambda \text{Now}4\lambda +9\lambda +16\lambda =29\Rightarrow \lambda =1$
So the coordinate of the foot of the perpendicular is $(2,-3,4)$