Question

Let $ABCD$ be a parallelogram and $\overrightarrow{AC},\overrightarrow{BD}$ are its diagonals Then, $\overrightarrow{AC}-\overrightarrow{BD}$ is

• A. $2\overrightarrow{AB}$
• B. $2\overrightarrow{BC}$
• C. $3\overrightarrow{AB}$
• D. $3\overrightarrow{BC}$

Answer 1

Answer: (A)

$2\overrightarrow{AB}$

We have $AB||CD$ and $BC||AD$
So, $\overrightarrow{AC}=\overrightarrow{AB}+\overrightarrow{BC}$ (addition theorem) and $\overrightarrow{BD}=\overrightarrow{BD}+\overrightarrow{AD}$ (addition theorem)
$\therefore$ $\overrightarrow{AC}-\overrightarrow{BD}=\overrightarrow{AB}+\overrightarrow{BC}-(\overrightarrow{BA}+\overrightarrow{AD})$
$=\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{AB}-\overrightarrow{AD}$
$=2\overrightarrow{AB}$