Let d = λ ( a × b ) + μ ( b × c ) + ν ( c × a ) , [ a b c ] = 8 1 , and d ⋅ ( a + b + c ) = 8 . Find λ + μ + ν .

Dotting d with c , a , b respectively gives 8 1 λ , 8 1 μ , 8 1 ν . Their sum is 8, so the answer is 64.

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Let $d = λ (a \times b) + μ (b \times c) + ν (c \times a), [a b c] = \frac{1}{8}$ , and $d \cdot (a + b + c) = 8$ . Find $λ + μ + ν$ .

Answer:

Solution:

Dotting $d$ with $c, a, b$ respectively gives $\frac{1}{8} λ, \frac{1}{8} μ, \frac{1}{8} ν$ . Their sum is 8, so the answer is 64.

Stream:JEESubject:MathematicsTopic:VectorSubtopic:STP

⏱ 2mℹ️ Source: QB

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