a,b,c are the position vectors of A,B,C respectively.Prove that( a x b)+(b x c)+(c x a) is a vector perpendicular to plane of triangle ABC.

Asked by HARSHA | 28th Mar, 2012, 08:50: AM

Expert Answer:

Let p = ( a x b)+(b x c)+(c x a) ,
Now , p is perpendicular to the plane only if AB.p = BC.p = CA.p = 0
 
Now AB.p = (b-a).p , On Solving we get , [b c a] - [b c a] = 0
Similarly we can prove it for other vectors too , hence proved.

Answered by  | 28th Mar, 2012, 10:43: AM

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