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Question

Prove that: a -b · b -c × c -a =0

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Solution

We have (a-b).(b-c) × (c-a) =(a-b) . ( b×c-b×a-c×c+c×a) (By distributive law) = ( a-b ) . ( b¯×c-b×a+c×a ) ( c×c=0)=( a-b ) . ( b¯×c+a×b+c×a ) = a.(b×c) +a.(a×b) +a.(c×a) - b.(b×c) -b.(a×b) - b.(c×a) (By distributive law)=abc +aab +aca -bbc -b a b -bca= abc +0+0-0-0-abc abc=bca = 0

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