Question

if 5a-3b-2c =0 and point
c divdes segment AB then,
I find the ratio of the point B
of division​

Answer 1

$\textbf{Concept:}$

$\text{External division:}$

$\text{The position of the point C which divides the line segment joining}$

$\text{the points A and B externally in the ratio m:n is}$

$\bf\overrightarrow{c}=\frac{m\overrightarrow{b}-n\overrightarrow{a}}{m-n}$

$\textbf{Given:}$

$5\overrightarrow{a}-3\overrightarrow{b}-2\overrightarrow{c}=\overrightarrow{0}$

$\implies\;5\overrightarrow{a}-3\overrightarrow{b}=2\overrightarrow{c}$

$\implies\;\frac{5\overrightarrow{a}-3\overrightarrow{b}}{5-3}=\overrightarrow{c}$

$\implies\;\frac{3\overrightarrow{b}-5\overrightarrow{a}}{3-5}=\overrightarrow{c}$

$\therefore\textbf{C divides AB externally in the ratio 3:5}$