The points with the co-ordinates $(2 a, 3 a)$ , $(3 b, 2 b)$ & $(c, c)$ are collinear.

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Solution

If the area of triangle is $0$ , then there will be no triangle, the points will be collinear,
$= 4 a b + 3 b c - 2 a c - 9 a b - 2 b c - 2 a c$
$= 4 a b - 3 b c - 2 b - 9 a b$
$= 4 a b - 9 a b + b c$
$= - 5 a b + b c$
$5 a b = b c$
$5 a = c$ .

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