Question

If the foot of the perpendicular from the origin to a plane is $P(a,b,c)$, the equation of the plane is-

• A. $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=3$
• B. $ax+by+cz=3$
• C. $ax+by+cz=a^2+b^2+c^2$
• D. $ax+by+cz=a+b+c$

Answer 1

The correct option is C $ax+by+cz=a^2+b^2+c^2$

Let $P(a,b,c)$ be the foot of the perpendicular from the origin to the plane, then direction ratios of
$OP$ are $a-0,b-0,c-0$ i.e. $a,b,c$.
So, the equation of the plane passing through $P(a,b,c)$ the direction ratios of the normal to which
are $a,b,c$ is
$a(x-a)+b(y-b)+c(z-c)=0$
$\Rightarrow$ $ax+by+cz=a^2+b^2+c^2$