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Question

If a+2b+3c=0 and a×b+b×c+c×ais equal to λ(b×c) then λ is equal to

A
3
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B
4
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C
5
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D
None of these
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Solution

The correct option is D None of these
Given
a+2b+3c=0
i.e., a=2b3c

Now
a×b+b×c+c×a=λ(b×c)
i.e., (2b3c)×b+b×c+c×(2b3c)=λ(b×c)
i.e., 2(b×b)3(c×b)+b×c2(c×b)3(c×c)=λ(b×c)
i.e., 3(b×c)+(b×c)+2(b×c)=λ(b×c) (b×b=c×c=0 and c×b=b×c)
i.e., 6(b×c)=λ(b×c)
λ=6

Hence the correct answer is Opt:[D]

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