Prove that (a-b).{(b-c)x(c-a)}=0 where a,b and c are vectors.

Asked by HARSHA | 28th Mar, 2012, 08:52: AM

Expert Answer:

The given expression can be written as ,
(a-b) .{ bxc - bxa - cxc +cxa }
 
= (a-b).{ bxc - bxa - 0 + cxa }
= { a.bxc - a.(bxa) +a.(cxa) -b.(bxc) - b.(bxa) - b.(cxa) }
 
= { [a b c] - 0 + 0 - 0 - 0 - [b c a] }
 
= [a b c] - [a b c] = 0

Answered by  | 28th Mar, 2012, 10:39: AM

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