If →r=α→b×→c+β→c×→a+γ→a×→b and [→a→b→c]=2 , then α+β+γ=
A
→r.(→b×→c+→c×→a+→a×→r)
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B
12→r(→a+→b+→c)
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C
2→r(→a+→b+→c)
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D
4
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Solution
The correct option is B12→r(→a+→b+→c) We have →r=α→b×→c+β→c×→a+γ→a×→b ⇒→r.→a=α→b×→c.→a+β→c×→a.→a+γ→a.×→b.→a →r.→a=α→b×→c.→a+0+0 →r.→a=α→b×→c.→a =α[→a→b→c] =2α from the question We have →r=α→b×→c+β→c×→a+γ→a+→b ⇒→r.→b=α→b×→c.→b+β→c×→a.→b+γ→a+→b.→b ⇒→r.→b=0+β→c×→a.→b+0 =β[→a→b→c] =2β We have →r=α→b×→c+β→c×→a+γ→a×→b ⇒→r.→c=α→b×→c.→c+β→c×→a.→c+γ→a×→b.→c →r.→c=0+0+γ→a×→b.→c =γ[→a→b→c] =2γ Adding α+β+γ=12[→r.→a+→r.→b+→r.→c] =12→r(→a+→b+→c)