The value of [→a−→b→b−→c→c−→a]+[→a×→b→b×→c→c×→a] equals?
A
[→a→b→c]
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B
[→a→b→c]2
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C
0
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D
−[→a→b→c]
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Solution
The correct option is C[→a→b→c] [(→a−→b)(→b−→c)(→c−→a)]+[→a×→b×→c(→c×→a]⇒{(→a−→b)×(→b−→c)}.(→c−→a)+[(a×b).(→c×→a)]⇒{→a×→b−→a×→c−→b×→b+→b×→c}.(→c−→a)+[abc]2⇒{→a×→b+→c×→a+→b×→c}.(→c×→a)+[abc]2⇒{[abc]+[abc]}+[abc]2[∴→a×→b=(→b×→a)][→a×→a=0]∴[abc]2