The correct option is C [#160;a #160;b #160;d]#160;c Let us take nbsp; a× nbsp;b nbsp;as nbsp; x nbsp; The question becomes ...

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Implicit Differentiation

a⃗×b⃗×c⃗×d⃗+[...

Question

$(\to a \times \to b) \times (\to c \times \to d) + [\to a \to b \to c] \to d =$

\to 0

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\to a

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[\to a \to b \to d] \to b

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[\to a \to b \to d] \to c

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Solution

The correct option is C $[\to a \to b \to d] \to c$
Let us take $¯ ¯ ¯ a \times ¯ ¯ b$ as $¯ ¯ ¯ x$
The question becomes $¯ ¯ ¯ x \times [¯ ¯ c \times ¯ ¯ ¯ d] + [¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] ¯ ¯ ¯ d$
$= (¯ ¯ ¯ x . ¯ ¯ ¯ d) ¯ ¯ c - (¯ ¯ ¯ x . ¯ ¯ c) ¯ ¯ ¯ d + [¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] ¯ ¯ ¯ d$
$= [¯ ¯ ¯ a ¯ ¯ b ¯ ¯ ¯ d] ¯ ¯ c - [¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] ¯ ¯ ¯ d + [¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] ¯ ¯ ¯ d$
$= [¯ ¯ ¯ a ¯ ¯ b ¯ ¯ ¯ d] ¯ ¯ c$

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