# A and B are two points with position vectors $2\overrightarrow{a}-3\overrightarrow{b}$ and $6\overrightarrow{b}-\overrightarrow{a}$ respectively.Write the position vector of a point P which divides the line segment AB internally in the ratio 1 : 2.

$\overrightarrow{OA}=2\overrightarrow{a}-3\overrightarrow{b}$
$\overrightarrow{OB}=6\overrightarrow{b}-\overrightarrow{a}$ and ration is 1:2
$\overrightarrow{OP}=\large\frac{m\overrightarrow{OB}+n\overrightarrow{OA}}{m+n}$
$\overrightarrow{OP}=\large\frac{(6\overrightarrow{b}-\overrightarrow{a})+2(2\overrightarrow{a}-3\overrightarrow{b})}{1+2}$
$=\large\frac{6\overrightarrow{b}-\overrightarrow{a}+4\overrightarrow{a}-6\overrightarrow{b}}{3}$
$\overrightarrow{op}=\large\frac{3\overrightarrow{a}}{3}=\overrightarrow{a}$