Question

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

Options

• \[4 \overrightarrow{AB}\]

• \[3 \overrightarrow{AB}\]
• \[2 \overrightarrow{AB}\]

   

• \[\overrightarrow{AB}\]

Answer 1

\[2 \overrightarrow{AB}\]
Given: ABCD, a parallelogram with diagonals AC and BD.
Then,

\[\overrightarrow{AC} = \overrightarrow{AB} + \overrightarrow{BC} \]

\[ \overrightarrow{AD} = \overrightarrow{AB} + \overrightarrow{BD} \]

\[ \Rightarrow \overrightarrow{BD} = \overrightarrow{AD} - \overrightarrow{AB}\]
∴ \[\overrightarrow{AC} - \overrightarrow{BD} = \overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{AD} + \overrightarrow{AB} = 2 \overrightarrow{AB}\]                        [∵ \[\overrightarrow{AD} = \overrightarrow{BC}\]]