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Question

If a,b,c are non-coplanar vectors and d=λa+μb+νc, then λ equal to


A

[d b c][b a c]

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B

[b c d][b c a]

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C

[b d c][a b c]

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D

[c b d][a b c]

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Solution

The correct option is B

[b c d][b c a]


d=λa+μb+νc[d b c]=d.b×c=λ a.b×c+μ b.b×c+ν c.b×c=λ[abc]+0+0=λ[abc]λ=[dbc][abc]=[bcd][bca]


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