If →r⋅^i=2→r⋅^j=4→r⋅^k and |→r|=√21, then vector →r is
A
4^i−2^j−^k
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B
4^i+2^j+^k
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C
−4^i−2^j−^k
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D
−4^i+2^j−^k
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Solution
The correct option is C−4^i−2^j−^k Let →r=x^i+y^j+z^k ∵→r⋅^i=2→r⋅^j=4→r⋅^k⇒x=2y=4z⋯(i)
also, |→r|=√21 ⇒x2+y2+z2=21⇒16z2+4z2+z2=21⇒z=±1
So, x=±4,y=±2
So, →r=4^i+2^j+^k or →r=−(4^i+2^j+^k)