Question

Find the position vector of a vector of a point R which divides the line joining two points P and Q whose position vectors are $(2a+b)$ and $9\overrightarrow{a}-3\overrightarrow{b})$ externally in the ratio $1:2$ also show that P is the mid point of the line segment $RQ$

Answer 1

$(2a+\overline{b})(\overline{a}-3\overline{b})$
$\frac{1(7bara-3\overline{b})-2(2\overline{a}+\overline{b})}{1-2},\frac{-3\overline{a}-5\overline{b}}{-1}=3\overline{a}+5\overline{b}$
$\therefore$ p.v. of R $(3\overline{a}+5\overline{b})$