If a- b- c- are three noncoplanar nonzero vectors and r- is any vector in space then a-b- - r-c- -b-c- r-a- - c-a- - r-b- is equal to

The correct option is A 2[ a⃗b⃗c⃗] r⃗ (a⃗×b⃗) × (r⃗×c⃗) = [a⃗b⃗c⃗ ] r⃗ [a⃗b⃗r⃗ ] c⃗ ......(1) (a⃗×c⃗) × (r⃗×a⃗ ) = [b⃗c⃗a⃗] r⃗ [b⃗c⃗r⃗ ] a⃗ ...

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Definition of Vector

If a⃗, b⃗, ...

Question

If $\to a, \to b, \to c$ are three noncoplanar nonzero vectors and $\to r$ is any vector in space then $(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)$ is equal to

2 [\to a \to b \to c] \to r

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3 [\to a \to b \to c] \to r

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[\to a \to b \to c] \to r

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none of these

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\to a, \to b, \to c

\to r

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)

\to a, \to b, \to c

\to r

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b) =

\to a, \to b, \to c

\to p, \to q, \to r

\to p = \frac{\to b \times \to c}{[\begin{matrix} \to b & \to c & \to a \end{matrix}]}

\to q = \frac{\to c \times \to a}{[\begin{matrix} \to c & \to a & \to b \end{matrix}]}

\to r = \frac{\to a \times \to b}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}

(\to a + \to b) . \to p + (\to b + \to c) . \to q + (\to c + \to a) . \to r

\to r = (\to a \times \to b) sin x + (\to b \times \to c) cos y + 2 (\to c \times \to a)

\to a \to b \to c

\to r

\to a + \to b + \to c

x^{2} + y^{2}

\to a, \to b, \to c

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}

\to q = \frac{\to c \times \to a}{[\to a \to b \to c]}

\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

(2 \to a + 3 \to b + 4 \to c) . \to p + (2 \to b + 3 \to c + 4 \to a) . \to q +

(2 \to c + 3 \to a + 4 \to b) . \to r =

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