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Question

Assertion :If a,b,c are three non-coplanar, non-zero vectors, then (a.a)b×c+(a.b)c×a+(a.c)a×b=[bca]a Reason: If the vectors a,b,c are non-coplanar, then so are b×c,c×a,a×b

A
Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
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B
Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
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C
Assertion is true but Reason is false
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D
Assertion is false but Reason is true
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Solution

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
As a,b,c are non-coplanar, b×c,c×a,a×b are also non-coplanar.
So, any vector can be expressed as a linear combination of these vectors.
Let a=λb×c+μc×a+va×b
a.a=λ[bca],a.b=μ[cab],a.c=v[abc]
a=(a.a)b×c[bca]+(a.b)c×a[cab]+(a.c)a×b[abc]
(a.a)b×c+(a.b)c×a+(a.c)a×b=[bca]a.

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