`A B C D` is a parallelogram with `A C` and `B D` as diagonals. Then, ` vec (A C)- vec (B D)=`

Options

A. a) `4 vec (A B)`
B. b) `3 vec (A B)`
C. c) `2 vec (A B)`
D. d) ` vec (A B)`

Answer

c) `2 vec (A B)`

Explanation

In `DeltaABC`.


`vec(AB)=vec a, vec(BC)=vec(AD)=vec b`


`vec a+vec b=vec(AC)`



In `DeltaABD`.


`vec a+vec (BD)=vecb`


`vec (BD)=vecb-vec a`



`vec (A C)- vec (B D)=vec a+vec b-(vecb-vec a)`


`vec (A C)- vec (B D)=2vec a`


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