The value of a-b-c- - a- b-c -b-c-a- - a- b-c -c-a-b- - a- b-c - is

The correct option is A 3 a·b×c/ [ abc ] +b·c×a/ [ abc ]+c·a×b/ [ abc ] =a·a'+b·b'+c·c' =3 ( as a·a'=b·b'=c·c'=1 ) ...

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Question

The value of $¯ ¯ ¯ a . \frac{¯ ¯ b \times ¯ ¯ c}{[¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c]} + ¯ ¯ b . \frac{¯ ¯ c \times ¯ ¯ ¯ a}{[¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c]} + ¯ ¯ c . \frac{¯ ¯ ¯ a \times ¯ ¯ b}{[¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c]}$ is

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[¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] = 1

\frac{¯ ¯ ¯ a . (¯ ¯ b \times ¯ ¯ c)}{(¯ ¯ c \times ¯ ¯ ¯ a) . ¯ ¯ b} + \frac{¯ ¯ b . (¯ ¯ c \times ¯ ¯ ¯ a)}{(¯ ¯ b \times ¯ ¯ ¯ a) . ¯ ¯ c} + \frac{¯ ¯ c . (¯ ¯ ¯ a \times ¯ ¯ b)}{(¯ ¯ b \times ¯ ¯ c) . ¯ ¯ ¯ a} =

\to a, \to b, \to c

\to a + \to b + \to c = \to 0

∣ ∣ \to a ∣ ∣ = 2, ∣ ∣ ∣ \to b ∣ ∣ ∣ = 3, ∣ ∣ \to c ∣ ∣ = 5,

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

∣ ∣ \to a ∣ ∣ = ∣ ∣ ∣ \to b ∣ ∣ ∣ = ∣ ∣ \to c ∣ ∣ = 1, \to a . \to b = \to b . \to c = \to c . \to a = \frac{1}{2}

[\to a, \to b, \to c] =

¯ ¯¯ ¯ A . (¯ ¯¯ ¯ B + ¯ ¯¯ ¯ C) = ¯ ¯¯ ¯ B . (¯ ¯¯ ¯ C + ¯ ¯¯ ¯ A) = ¯ ¯¯ ¯ C . (¯ ¯¯ ¯ A + ¯ ¯¯ ¯ B) = 0

| ¯ ¯¯ ¯ A | = 3, | ¯ ¯¯ ¯ B | = 4

| ¯ ¯¯ ¯ C | = 5

| ¯ ¯¯ ¯ A + ¯ ¯¯ ¯ B + ¯ ¯¯ ¯ C | =

\to a, \to b, \to c

\to a + \to b + \to c = 0

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

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