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Points A( vec a),B( vec b),C( vec c)a n ...

Points `A( vec a),B( vec b),C( vec c)a n dD( vec d)` are relates as `x vec a+y vec b+z vec c+w vec d=0` and `x+y+z+w=0,w h e r ex ,y ,z ,a n dw` are scalars (sum of any two of `x ,y ,zn a dw` is not zero). Prove that if `A ,B ,Ca n dD` are concylic, then `|x y|| vec a- vec b|^2=|w z|| vec c- vec d|^2dot`

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