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Sum of n Terms

If a × b × ...

Question

If $\to a \times (\to b \times \to c) + \to b \times (\to c \times \to a) = λ_{1} \to a + λ_{2} \to b + λ_{3} \to c$ then $λ_{1} + λ_{2} + λ_{3} =$

A

- \to b . \to c + \to a . \to c

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B

\to a . \to c + \to b . \to c

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C

\to a . \to b + \to b . \to c + \to c . \to a

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D

none of these

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Solution

The correct option is A $- \to b . \to c + \to a . \to c$
$\begin{matrix} \to a \times (\to b \times \to c) + \to b \times (\to c \times \to a) = (\to a . \to c) \to b - (\to a . \to b) \to c + (\to b . \to a) \to c - (\to b . \to c) \to a = - (\to b . \to c) \to a + (\to a . \to c) \to b + (\to b . \to a - \to a . \to b) \to c \equiv λ_{1} \to a + λ_{2} \to b + λ_{3} \to c λ_{1} + λ_{2} + λ_{3} = \to a . \to c - \to b . \to c o r - \to b . \to c + \to a . \to c H e n c e, o p t i o n A i s c o r r e c t a n s w e r . \end{matrix}$

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