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Position Vector

L and M are t...

Question

L and M are two points with position vectors $2 \to a - \to b$ and $\to a + 2 \to b$ respectively. Write the position vector of a point N which divides the line segment LM in the ratio 2 : 1 externally.

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Solution

$- - \to O L = 2 \to a - \to b$ and $- - \to O M = \to a + 2 \to b$
Since $N$ divides $L M$ in $2 : 1$ externally, so
$- - \to O N = \frac{1. - - \to O L - 2. - - \to O M}{1 - 2} = 2. (2 \to a - \to b - 1. (\to a + 2 \to b))$
Therefore, $- - \to O N = 3 \to a - 4 \to b$

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