Point $R$ divides the line segment joining $A(\vec a)$ and $B(\vec b)$ **internally** in the ratio $m : n$. The position vector of $R$ is:
A$\dfrac{m\vec a + n\vec b}{m + n}$
B$\dfrac{m\vec b + n\vec a}{m + n}$
C$\dfrac{m\vec b - n\vec a}{m - n}$
D$\dfrac{\vec a + \vec b}{m + n}$
Answer & Solution
Correct answer: B. $\dfrac{m\vec b + n\vec a}{m + n}$
Section formula (internal): $\vec r = (m\vec b + n\vec a)/(m + n)$. The point $R$ is closer to $B$ as $m$ increases — note $m$ multiplies $\vec b$. (External division uses $(m\vec b - n\vec a)/(m - n)$.)
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