Question

The plane $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=k$, meets the coordinate axes at A, B, C such that the centroid of the triangle ABC is the point (a, b, c). Then k is

• A. 3
• B. 2
• C. 1
• D. 5

Answer 1

The correct option is A 3

$\because \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=k\Rightarrow \frac{x}{ak}+\frac{y}{bk}+\frac{z}{ck}=1$
$\therefore$ Coordinates of A, B and C are (ak, 0, 0), (0, bk, 0) and (0, 0, ck) respectively $\therefore$ Centroid of ∆ABC is (a, b, c) $\therefore a=\frac{ak+0+0}{3}\Rightarrow k=3$