If ` vec a\ a n d\ vec b` represent two adjacent sides of a parallel then write vectors representing its diagonals.

Explanation

Considering a parallelogram `ABCD`
we see
`vec{A B}=vec{A^{prime} B^{prime}}=vec{a} cdot vec{A A^{prime}}=vec{B B^{prime}}=vec{b} cdot vec{A B^{prime}}=vec{c} text { and }
vec{B A^{prime}}=vec{d}`


Using parallelogram law of vector addition, we can say that


`vec{a}+vec{b}=vec{c} text { and } vec{a}+vec{d}=vec{b} text { or } vec{d}=vec{b}-vec{a}`


Also, `vec{c}` and `vec{d}` are the diagonals of the parallelogram.

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