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Question

If the vectors a,b and c form the sides BC, CA and AB respectively of a Δ ABC, then

A
a.b+b.c+c.a=0
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B
a×b=b×c=c×a
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C
a. b=b. c=c. a
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D
a×b+b×c=c×a=0
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Solution

The correct option is B a×b=b×c=c×a
By triangle law, a+b+c=0

Taking cross product by a,b,c respectively,
a×(a+b+c)=a×0=0a×a+a×b+a×c=0a×b=c×a [a×a=0]Similarly, a×b=b×ca×b=b×c=c×a

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