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Question

# Let →p,→q,→r be three mutually perpendicular vectors of the same magnitude. If a vector →x satisfies the equation →p×((→x−→q)×→p)+→q×((→x−→r)×→q)+→r×((→x−→p)×→r)=0. Then →x is given by.

A
12(p+q2r)
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B
13(q+q+r)
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C
12(p+q+r)
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D
13(2p+qr)
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Solution

## The correct option is C 12(→p+→q+→r)Consider the problem Let |p|=|q|=|r|=cAndp.q=0=p.r=q.rp×|(x−q)×p|+q×|(x−r)×q|+r×|(x−p)×r|=0⇒(p.p)(x−q)−{p.(x−q)}p+.........=0⇒c2(x−q+x−r+x−p)−(p.x)p−(q.x)q−(r.x)r=0⇒c2{3x−(p+q+r)}−[(p.x)p+(q.x)q+(r.x)r]=0which is satisfied by x=12(p+q+r)Hence, Option C is the correct answer.

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