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Question

Let a,b and c be mutually perpendicular vectors of the same magnitude.If a vector x satisfies the equation
a×[(xb)×a]+b×[(xc)×b]+c×[(xa)×c]=0, then x is given by

A
12(a+b+c)
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B
13(2a+b+c)
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C
13(a+b+c)
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D
12(a+b2c)
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Solution

The correct option is A 12(a+b+c)
Let a=b=c=λ, then
a2(xb)[a.(xb)]+b2(xc)[b.(xc)]b+c2(xa)c(xa]c=0
λ2(3xabc)[(a.x)a(b.x)b(c.x)c](a.b)a+(b.c)b+(c.a)c=0
λ2(3xabc)λ2x=0
⎢ ⎢ ⎢ ⎢a=a.xa2a+b.xb2b+c.xc2c⎥ ⎥ ⎥ ⎥
x=12(a+b+c)

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