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

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Solution

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

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The plane xa+yb+zc=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

The correct option is A 3∵xa+yb+zc=k⇒xak+ybk+zck=1 ∴ Coordinates of A, B and C are (ak, 0, 0), (0, bk, 0) and (0, 0, ck) respectively ∴ Centroid of ∆ABC is (a, b, c) ∴a=ak+0+03⇒k=3

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