Q. If the foot of the perpendicular from the origin to a plane is $P(a,\ b,\ c)$, the equation of the plane is
A) $\frac{x}{a} + \frac{y}{b} + \frac{\mathcal{z}}{c} = 3$
B) $ax + by + c\mathcal{z} = 3$
C) $ax + by + c\mathcal{z} = a^{2} + b^{2} + c^{2}$
D) $ax + by + c\mathcal{z} = a + b + c$
Explanation
(c)
Direction ratios of $OP$ are $(a,\ b,\ c)$
Therefore, equation of the plane is
$a(x - a) + b(y - b) + c\left( \mathcal{z} - c \right) = 0$
i.e., $xa + yb + \mathcal{z}c = a^{2} + b^{2} + c^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.