Question

If $\overrightarrow{OA}=\overrightarrow{a}$ and $\overrightarrow{OB}=\overrightarrow{b}$, then $\overrightarrow{BA}$ is:

• (A) $\overrightarrow{a}+\overrightarrow{b}$
• (B) $\overrightarrow{a}$
• (C) $\overrightarrow{b}$
• (D) $\overrightarrow{a}-\overrightarrow{b}$

Answer 1

The Correct Option is D

Explanation:
If $\overrightarrow{OA}$ is the position vector of $A$ and $\overrightarrow{OB}$ is position vector of $B$ then-$\overrightarrow{AB}=$ Position Vector of $B-$ Position Vector of $A$ ......(I)$\overrightarrow{BA}=$ Position Vector of $A-$ Position Vector of $B$ ......(II)Given, $\overrightarrow{OA}=\overrightarrow{a}$ and $\overrightarrow{OB}=\overrightarrow{b}$Then, by equation (II)$\overrightarrow{BA}=$ position vector of $A-$ position vector of $B$$\overrightarrow{BA}=\overrightarrow{OA}-\overrightarrow{OB}$$\overrightarrow{BA}=\overrightarrow{a}-\overrightarrow{b}$Hence, the correct option is (D).