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The position vectors a,b,c and d {all in vectors} of four points A,B,C and D

 

on a plane are such that

 

(a-d).(b-c)=(b-d).(c-a)=0,    {all in vectors}

 

then the pont D is

 

1]centroid of ABC

 

2] ortho centre of ABC

 

3]circumcentre  of ABC

 

4]None of these.

 

plzz help ,and  post a detailed solution plz and i want theoritical proof plzz as it would increase our mind to think better for other problems like these