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Section Formula

If a →, b...

Question

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

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Solution

given $\to O A = \to a, \to O B = \to b$
$\to A C = 3 \to A B$ and $B D = 2 B A$ to find $: \to O C$ and $\to O D$
$\to O C - \to O A = 3 (\to O B - \to O A)$
$\to O C - \to a = 3 (\to b - \to a)$
$\to O C = 3 \to b - 2 \to a$
podition vector of $C = 3 \to b - 2 \to a$
$\to B D = 2 \to B A$
$\to O D - \to O B = 2 (\to O A - \to O B)$
$\to O D - \to b = 2 (\to a - \to b)$
$\to O D = 2 \to a - \to b$
position vector of $\to O D = 2 \to a - \to b$

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