The position vector of a point R which divides the line joining the points A(-2, 1, 3) and B(3, 5, -2) internally in the ratio 2 : 1, is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{4}{3}\hat{\imath}+\displaystyle\frac{11}{3}\hat{\jmath}-\displaystyle\frac{1}{3}\hat{k} \)
For a point dividing AB internally in the ratio m : n,
\( \displaystyle \vec{r}=\frac{m\vec{b}+n\vec{a}}{m+n} \)
Here m = 2, n = 1, \( \vec{a}=-2\hat{\imath}+\hat{\jmath}+3\hat{k} \) and \( \vec{b}=3\hat{\imath}+5\hat{\jmath}-2\hat{k} \).
\( \displaystyle 2\vec{b}+\vec{a}=(6-2)\hat{\imath}+(10+1)\hat{\jmath}+(-4+3)\hat{k} \)
\( \displaystyle =4\hat{\imath}+11\hat{\jmath}-\hat{k} \)
\( \displaystyle \vec{r}=\frac{4\hat{\imath}+11\hat{\jmath}-\hat{k}}{3} \)
\( \displaystyle =\frac{4}{3}\hat{\imath}+\frac{11}{3}\hat{\jmath}-\frac{1}{3}\hat{k} \)
Tip: In the section formula the ratio number m multiplies the far end B; swapping them (\( 2\vec{a}+\vec{b} \)) gives the point dividing AB in the ratio 1 : 2 instead.
NCERT (2026-27 edition):
Section Formula
