Question

If ABCD is a parallelogram and AC and BD are its diagonals, then $\overrightarrow{AC} + \overrightarrow{BD}$ is:

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

Hint:

In a parallelogram, the sum of the diagonals equals twice one side vector.

Answer 1

The Correct Option is B

Let’s use position vectors: \[ \overrightarrow{AC} = \overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AB} + \overrightarrow{AD}. \overrightarrow{BD} = \overrightarrow{BC} + \overrightarrow{CD} = \overrightarrow{BA} + \overrightarrow{AD}. \text{Better to use:} \overrightarrow{AC} + \overrightarrow{BD} = 2\overrightarrow{AB}. \] So, \[ \overrightarrow{AC} + \overrightarrow{BD} = 2\overrightarrow{AB}. \]