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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`

Text Solution

Verified by Experts

The correct Answer is:
`veca`
Let `vecalpha, vecbeta,vecgamma` be any three mutually perpendicular non-coplanar, unit vectors and `veca` be any vector, then
`veca= (veca.vecalpha)vecalpha+ (veca.vecbeta)+(veca.vecgamma)vecgamma`
Here `vecb, vecc` are two mutually perpendicular vectors,
therefore, `vecb , vecc and (vecb xx vecc)/(|vecb xx vecc|)` are three mutually
Perpendicular non-coplanaar unit vectors. Hence
`veca=(veca .vecb)vecb+(veca.vecc)vecc`
`+(veca.(vecbxxvecc)/(|vecb xx vecc|))(vecb xx vecc)/(|vecb xx vecc|)`
`(veca.vecb)vecb+(veca.vecc)vecc`
`+(veca.(vecbxxvecc))/(|vecb xx vecc|^(2))(vecbxxvecc)`
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