If ` vec a ,\ vec b ,\ vec c` and ` vec d` are the position vectors of points `A , B ,\ C ,\ D` such that no three of them are collinear and ` vec a+ vec c= vec b+ vec d`, then `A B C D` is a

Options

A. a) rhombus
B. b) rectangle
C. c) square
D. d) parallelogram

Answer

d) parallelogram

Explanation

` vec a+ vec c= vec b+ vec d`


` vec a- vec b= vec d- vec c`


`vec(BA)=vec(CD)`


`|vec(BA)|=|vec(CD)|`


`BA` is parallel to `CD`



` vec a+ vec c= vec b+ vec d`


` vec a- vec d= vec c- vec b`


`vec(AD)=vec(BC)`


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