Question
Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin, then −−→OA+−−→OB+−−→OC+−−→OD equals
Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin, then −−→OA+−−→OB+−−→OC+−−→OD equals
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Solution
The correct option is D 4−−→OP
Since, the diagonals of a parallelogram bisect each other. Therefore, P is the middle point of AC and BD both.
∴−−→OA+−−→OC=2−−→OPand−−→OB+−−→OD=2−−→OP⇒−−→OA+−−→OB+−−→OC+−−→OD=4−−→OP
Since, the diagonals of a parallelogram bisect each other. Therefore, P is the middle point of AC and BD both.
∴−−→OA+−−→OC=2−−→OPand−−→OB+−−→OD=2−−→OP⇒−−→OA+−−→OB+−−→OC+−−→OD=4−−→OP
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