P is the pointegral of integralersection of the diagonals of... | MATH - VECTOR OR CROSS PRODUCT OF TWO VECTORS AND ITS APPLICATIONS | SolveeIt | Solveeit

Today, August 24

Question

P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then

$\overset{\rightarrow}{OA} + \overset{\rightarrow}{OB} + \overset{\rightarrow}{OC} + \overset{\rightarrow}{OD} =$

A

$\overset{\rightarrow}{OP}$

B

$2\overset{\rightarrow}{OP}$

C

$3\overset{\rightarrow}{OP}$

D

$4\overset{\rightarrow}{OP}$

Answer

$4\overset{\rightarrow}{OP}$

Explanation

Solution

We know that P will be the midpoint of AC and BD

$\therefore$ $\overset{\rightarrow}{OA} + \overset{\rightarrow}{OC} = 2\overset{\rightarrow}{OP}$ ......(i)

and $\overset{\rightarrow}{OB} + \overset{\rightarrow}{OD} = 2\overset{\rightarrow}{OP}$ …..(ii)

Adding (i) and (ii), we get, $\overset{\rightarrow}{OA} + \overset{\rightarrow}{OB} + \overset{\rightarrow}{OC} + \overset{\rightarrow}{OD} = 4\overset{\rightarrow}{OP}.$