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

We can draw a diagram with the given details.

Please refer to video to see the diagram.

It is given that,

`vec(AP) +vec(PB) +vec(PD) = vec(PC) `

`=>vec(AP) +vec(PB) = vec(PC) - vec(PD)->(1)`

Now, in `Delta PDC`,

`vec(PD)+vec(DC) = vec(PC)`

`=>vec(DC) = vec(PC) - vec(PD)->(2)`

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