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Vector Algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra1 Mark
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 (internally) 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 internally in the ratio 2 : 1 is
$\vec{OR}=\frac{2(\vec{a}+\vec{b})+(3 \vec{a}-2 \vec{b})}{2+1}=\frac{5 \vec{a}}{3}$

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