If `P` is a point and `A B C D` is a quadrilateral and ` vec A P+ vec P B+ vec P D= vec P C` , show that `A B C D` is a parallelogram.

Explanation

Here, it is given that,A B C D is quadrilateral

P is a point


`vec{{AP}}+vec{{PB}}+vec{{PD}}=vec{{PC}} `

`Rightarrow vec{{AP}}+vec{{PB}}=vec{{PC}}-vec{{PD}}=vec{{DC}} `

`Rightarrow vec{{AB}}=vec{{DC}}`

so from (i)

`vec{{AD}}+vec{{PB}}+vec{{PD}}=vec{{PC}} `

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