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Question

If [abc]=k, where k0, then [(b×c)×(c×a)(c×a)×(a×b)(a×b)×(b×c)]=

A
k
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B
k2
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C
k3
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D
k4
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Solution

The correct option is C k4
We have
(¯bׯc)×(¯cׯa)=[¯a¯b¯c]¯c
Similarly, (¯cׯa)×(¯aׯb)=[¯c¯a¯b]¯a
and (¯aׯb)×(¯bׯc)=[¯a¯b¯c]¯b
Removing the scalar triple product terms out of the bracket, we get [¯a¯b¯c]3[¯c¯a¯b]=[¯a¯b¯c]4
So k4

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