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Question

Let a=i+j+k,c=jk. If b is a vector satisfying a×b=c and a.b=3, then b is

A
13(5i+2j+2k)
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B
13(5i2j2k)
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C
(3i2jk)
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D
13(3ijk)
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Solution

The correct option is B 13(5i+2j+2k)
Now,
a×b=∣ ∣ ∣ˆiˆjˆk111b1b2b3∣ ∣ ∣=ˆi(b3b2)ˆj(b3b1)+ˆk(b2b1)=ˆjˆkb3b2=1............(1)b3b1=1.............(2)Substracting(1)(2)weget,b3b2=0b3=b2a×b=b1+b2+b3=3=b1+b2+b2=3=b1+2b2=3

Solving then we get b1=53,b2=23,b3=23
Hence,
b=13(5i+2j+2k)

Hence, this is the answer.

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