Consider two points P and Q with position vectors OP=3 a-2 b and … - Vidyadip

Question

Consider two points P and Q with position vectors $\vec{OP}=3 \vec{a}-2 \vec{b}$ and $\vec{OQ}=\vec{a}+\vec{b}$.
Find the position vector (externally) of a point R which divides the line joining P and Q in the ratio 2 : 1.

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Answer

The position vector of the point R dividing the join of P and Q externally in the ratio 2 : 1 is
$\vec{OR}=\frac{2(\vec{a}+\vec{b})-(3 \vec{a}-2 \vec{b})}{2-1}=4 \vec{b}-\vec{a}$

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