ABCD is a parallelogram with AC and BD as diagonals. Then, AC - B… - Vidyadip

MCQ

ABCD is a parallelogram with AC and BD as diagonals. Then, $\overrightarrow{\text{AC}}-\overrightarrow{\text{BD}}=$

A
$4\overrightarrow{\text{AB}}$
B
$3\overrightarrow{\text{AB}}$
✓
$2\overrightarrow{\text{AB}}$
D
$\overrightarrow{\text{AB}}$

✓

Answer

Correct option: C.

$2\overrightarrow{\text{AB}}$

Given: ABCD, a parallelogram with diagonals AC and BD. Then,

$\overrightarrow{\text{AC}}=\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}$

$\overrightarrow{\text{AD}}=\overrightarrow{\text{AB}}+\overrightarrow{\text{BD}}$

$\Rightarrow\ \overrightarrow{\text{BD}}=\overrightarrow{\text{AD}}-\overrightarrow{\text{AB}}$

$\therefore\overrightarrow{\text{AC}}-\overrightarrow{\text{BD}}=\overrightarrow{\text{AB}}+\overrightarrow{\text{BC}}-\overrightarrow{\text{AD}}+\overrightarrow{\text{AB}}=2\overrightarrow{\text{AB}}$ $\Big[\because\ \overrightarrow{\text{AD}}=\overrightarrow{\text{BC}}\Big]$

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