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Question

Let r be a vector perpendicular to a+b+c, where [abc]=2. If r=l(b×c)+m(c×a)+n(a×b), then (l + m + n) is equal to

A
2
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B
1
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C
0
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D
none of these
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Solution

The correct option is C 0
Given,
ra+b+c
i.e.
ra+rb+rc=0..........(1)&[a.b.c]=2
Now, ATQ
r=l(b×c)+m(c×a)+n(a×b)r.a=l(b×c).a=l[a×b×c]........(2)
We know that,
(b×c).a=[a×b×c]&[a×b×c]=0
Similarly,
r.b=m[a×b×c]..........(3)r.c=n[a×b×c]..........(4)
From (2)+(3)+(4) we get.
r.a+r.b+r.c=(l+m+n)[a×b×c]l+m+n=0 from equation (1)
Option C is correct answer.

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