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Question

If A=(1,1,1) and C=(0,1,1) are given vectors and B is a vector satisfying A×B=C and AB=3, then 9|B|2 is equal to

A
33
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B
22
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C
44
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D
55
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Solution

The correct option is D 33
Let B=(x,y,z), so that x+y+z=3,
Also
jk=C=∣ ∣ijk111xyz∣ ∣
=(zy)i+(xz)j+(yx)k
Hence z=y,xz=1 and xy=1. That is, z=y and x=1+y,
Therefore, 1+y+y+y=3, Thus y=2/3,z=2/3 and x=1+2/3=5/3
So 9|B|2=25+4+4=33

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