If ABCD be a parallelogram and M be the point of intersection of the diagonals. If O is any point, then overset→ mathopOA + overset→ mathopOB + overset→ mathopOC + overset→ mathopOD is

Question

If ABCD be a parallelogram and M be the point of intersection of the diagonals. If O is any point, then overset→ mathopOA + overset→ mathopOB + overset→ mathopOC + overset→ mathopOD is (A) 3 vecOM (B) 4 vecOM (C)  vecOM (D) 2 vecOM

Tardigrade Admin · Accepted Answer

We know that the diagonals of a parallelogram bisect each other. Therefore, M is the mid point of AC and BD both. ∴ OA+OC=2OM text and text OB+OD=2OM ⇒ OA+OB+OC+OD=4OM

Q. If $A BC D$ be a parallelogram and $M$ be the point of intersection of the diagonals. If $O$ is any point, then $O A \to + OB \to + OC \to + O D \to$ is

$3 OM$

$4 OM$

$OM$

$2 OM$

$\frac{1}{2} OM$

We know that the diagonals of a parallelogram bisect each other. Therefore, M is the mid point of AC and BD both.
$∴$ $O A + OC = 2 OM an d OB + O D = 2 OM$
$\Rightarrow$ $O A + OB + OC + O D = 4 OM$

Q. If ABCD be a parallelogram and M be the point of intersection of the diagonals. If O is any point, then OA→+OB→+OC→+OD→ is

3OM

4OM

OM

2OM

21​OM

We know that the diagonals of a parallelogram bisect each other. Therefore, M is the mid point of AC and BD both. ∴ OA+OC=2OMandOB+OD=2OM ⇒ OA+OB+OC+OD=4OM