Using the vector equation of the straight line passing through two points, prove that the points whose vectors are $a, b$ and $(3 a - 2 b)$ are collinear.

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Solution

Let $A, B$ and $C$ are the points whose position vectors are $\to a$ , $\to b$ and $\to c$
$\to A B = \to b - \to a$
$\to B C = 3 \to a - 2 \to b - \to a = - 2 (\to b - \to a)$
$\Rightarrow \to A C = - 2 \to A B$
Hence $\to a$ , $\to b$ and $\to c$ are collinear.

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