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Section Formula

If a , b ...

Question

If $\to a$ , $\to b$ are the vectors of A , B respectively, find the position vector of a point C. AB produced such that AC = 3AB and that a point D in BA produced such that BD = 2BA

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Solution

Let position vector of $C = \to c$
Let position vector of $D = \to d$
$\to A C = \to c - \to a$
$\to A B = \to b - \to a$
$\to B D = \to d - \to b$
$\to B A = \to a - \to b$
$A C = 3 A B$
$\Rightarrow \to c - \to a = 3 (\to b - \to a)$
$\Rightarrow \to c - \to a = 3 \to b - 3 \to a$
$\Rightarrow \to c = 3 \to b - 2 \to a$
$\Rightarrow \to B D = 2 \to B A$
$\Rightarrow \to d - \to b = 2 (\to b - \to a)$
$\Rightarrow \to d - \to b = 2 \to b - 2 \to a$
$\Rightarrow \to d = 3 \to b - 2 \to a$

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