In $ riangle O A C$, if $B$ is the mid-point of side $A C$ and $\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}$, then $\mathbf{O C}$ is equal to

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In $	riangle O A C$, if $B$ is the mid-point of side $A C$ and $\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}$, then $\mathbf{O C}$ is equal to

Aicharya · Accepted Answer

Given, $\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}$

$ \begin{aligned} & \text { In } \triangle O A B, \mathbf{O A}+\mathbf{A B}+\mathbf{B O}=0 \\ & \begin{aligned} \Rightarrow \quad \mathbf{A B} & =-\mathbf{a}-\mathbf{B O}=-\mathbf{a}-(\mathbf{b}) \\ & =-\mathbf{a}+\mathbf{b} \quad[\because \mathbf{O B}=\mathbf{b} \quad \therefore \mathbf{B O}=-\mathbf{b}] \\ \because \quad \mathbf{A C} & =2 \mathbf{A B}=2 \mathbf{b}-2 \mathbf{a} \end{aligned} \end{aligned} $ Now, in $\triangle O A C$, $ \begin{aligned} & & \mathbf{O A}+\mathbf{A C}+\mathbf{C O} & =0 \\ \Rightarrow & & \mathbf{a}+2 \mathbf{b}-2 \mathbf{a}-\mathbf{O C} & =0 \\ \Rightarrow & & \mathbf{O C} & =2 \mathbf{b}-\mathbf{a} \end{aligned} $

In $\triangle O A C$, if $B$ is the mid-point of side $A C$ and $\mathbf{O A}=\mathbf{a}, \mathbf{O…

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