The centroid of the triangle formed by (a, b), (b, c), (c, a) is the origin and a³ + b³ + c³ = kabc, then k is

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Solution

Q.
The centroid of the triangle formed by $(a, b), (b, c), (c, a)$ is the origin and $a^{3} + b^{3} + c^{3} = k a b c,$ then $k$ is _______.

Ans.
(3)

$Given, G = (\frac{a + b + c}{3}, \frac{a + b + c}{3}) = (0, 0)$

$\Rightarrow a + b + c = 0$

$\Rightarrow a^{3} + b^{3} + c^{3} = 3 a b c$

$\Rightarrow k = 3$

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