Plane a x + b y + c z = 1 intersect axes in A , B , C respectively. If G \left(\right. \frac{1}{6} , - \frac{1}{3} , 1 \left.\right) is a centroid of \triangle A B C then a + b + 3 c = ________

Engineering

Mathematics

Line of Greatest Slope

Question

Plane

a x + b y + c z = 1

intersect axes in

A, B, C

respectively. If

G (\frac{1}{6}, - \frac{1}{3}, 1)

is a centroid of

△ A B C

then

a + b + 3 c =

_________.

\frac{4}{3}

4

2

\frac{5}{6}

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let

A (\frac{1}{a}, 0, 0) B (0, \frac{1}{b}, 0) C (0, 0, \frac{1}{c})

c e n t r o i d \Rightarrow (\frac{1}{3 a}, \frac{1}{3 b}, \frac{1}{3 c}) = (\frac{1}{6}, \frac{- 1}{3}, 1)

On comparing we get,

3 a = 6 \Rightarrow a = 2 3 b = - 3 \Rightarrow b = - 1 3 c = 1 \Rightarrow c = \frac{1}{3}

∴ a = 2, b = - 1, c = \frac{1}{3}

∴ a + b + 3 c = 2

Only (C) is correct.

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