Question

A plane meets the coordinate axes at A, B, C and the foot of the perpendicular from the origin O to the plane is P, OA = a, OB = b, OC = c. If P is the centroid of the triangle ABC, then –

• A. a + b + c = 0
• B. |a| = |b| = |c|
• C. $\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$ = 0
• D. None of these

Answer 1

Answer: (B)

|a| = |b| = |c|

Answer 2

Let equation of the plane is

$\frac{x}{a} + \frac{y}{b} + \frac{z}{c}$ = 1 … (1)

Co-ordinates of P is$\left( \frac{a}{3},\frac{b}{3},\frac{c}{3} \right)$

Q OP is ^ to the plane

\ OP is parallel to normal to the plane (1)

\ $\frac{a/3}{1/a}$ = $\frac{b/3}{1/b}$ = $\frac{c/3}{1/c}$

Ž a² = b² = c²

Ž |a| = |b| = |c|.