ABCD is a parallelogram and O is the point of intersection of its diagonals. Then \(\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}\) is equal to
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\vec{0}\)
The diagonals of a parallelogram bisect each other, so O is the mid-point of AC and of BD. Hence \(\overrightarrow{OA}\) and \(\overrightarrow{OC}\) have equal length and opposite directions:
\(\overrightarrow{OC} = -\overrightarrow{OA}, \quad \overrightarrow{OD} = -\overrightarrow{OB}\)
\(\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD} = \overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{OA}-\overrightarrow{OB} = \vec{0}\)