If →a+2b+3c=0 , then →a×→b+→b×→c+→c×→a is equal to
A
6(b×c)
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B
6(¯¯c×→a)
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C
6(→aׯ¯b)
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D
none of these
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Solution
The correct option is A 6(b×c) ¯¯¯a+2b+3c=0¯¯¯a×(¯¯¯a+2b+3c)=02a×b+3¯¯¯a×c=02(¯¯¯aׯ¯b)=3(¯¯cׯ¯¯a)b×(a+2b+3c)=0b×a+2b×b+3b×c=03(b×c)=a×b∴a×b+b×c+c×a=3(b×c)+(b×c)+23(a×b)=3(b×c)+(b×c)+23×3(b×c)=6(b×c)OptionAiscorrectanswer.