Let $O A B C$ be a parallelogram with $O$ at the origin and $O C$ a diagonal. Let $D$ be the midpoin

Question

Let $O A B C$ be a parallelogram with $O$ at the origin and $O C$ a diagonal. Let $D$ be the midpoint of $O A$. Using vector methods prove that $B D$ and $C O$ intersect in the same ratio.\

Professor PC Thomas Classes · Answer

Let $\overrightarrow{O A}=\vec{a}, \overrightarrow{O B}=\vec{b}, \overrightarrow{O C}=\vec{a}+\vec{b}$,\ $\overrightarrow{O D}=\frac{\vec{a}}{2}$\ $\overrightarrow{O P}=\frac{\lambda(0)+1(\vec{a}+\vec{b})}{\lambda+1}$\ $\overrightarrow{O P}=\frac{\vec{a}+\vec{b}}{\lambda+1}, \overrightarrow{O P}=\frac{\mu\left(\frac{\vec{a}}{2}ight)+\vec{b}}{\mu+1}$\ we get $\lambda=\mu=2$\ $	herefore \quad$ The required ratio is $2: 1$\