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If vec a , vec b , vec c , vec d are th...

If ` vec a` ,` vec b` ,` vec c` ,` vec d` are the position vector of point `A , B , C` and `D` , respectively referred to the same origin `O` such that no three of these point are collinear and ` vec a` + ` vec c` = ` vec b` + ` vec d` , than prove that quadrilateral `A B C D` is a parallelogram.

A

square

B

rhombus

C

rectangle

D

parallelogram

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `a+c=b+d`
`implies(1)/(2)(a+c)=(1)/(2)(b+d)`
Here, mid-points of AC and BD coincide, where AC and BD are diagonals. In addition, we know that, diagonals of a parallelogram bisect each other.
Hence, quadrilateral is parallelogram.
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