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Find a unit vector perpendicular to each...

Find a unit vector perpendicular to each of the vector ` vec a+ vec b` and ` vec a- vec b` , where ` vec a=3 hat i+2 hat j+2 hat k` and ` vec b= hat i+2 hat j-\ 2 hat k`

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The correct Answer is:
`= pm(2)/(3)hat(i)pm (2)/(3)hat(j)pm(1)/(3)hat(k)`.
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