3D Geometry
Planes
MMTS_Full_Test_17
Grade 12
Question:
A plane meets coordinate axes at $A$, $B$, $C$ such that centroid of $\triangle ABC$ is at $(p,q,r)$. Equation of plane is
$\dfrac{x}{p}+\dfrac{y}{q}+\dfrac{z}{r}=3$
$\dfrac{x}{3p}+\dfrac{y}{3q}+\dfrac{z}{3r}=1$
$\dfrac{x}{p}+\dfrac{y}{q}+\dfrac{z}{r}=1$
Both 1 and 2
Step-by-Step Solution
Key Concept: $A=(3p,0,0)$, $B=(0,3q,0)$, $C=(0,0,3r)$; plane: $x/(3p)+y/(3q)+z/(3r)=1$
Both options 1 and 2 are correct and equivalent.
Correct Answer: 1