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If vec b is not perpendicular to vec c...

If ` vec b` is not perpendicular to ` vec c ,` then find the vector ` vec r` satisfying the equation ` vec rxx vec b= vec axx vec b` and `vec r. vec c=0.`

Text Solution

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Given `vecrxxvecb=vecaxxvecbRightarrow (vecr-veca)xxvecb=0`
Hence, (`vecr - veca) and vecb` are parallel.
`Rightarrow vecr-veca=tvecb`
`vecr.vecc=0`
Therefore, taking dot product of (i) by `vecc`, we get `vecr.vecc -veca.vecc=t(vecb .vecc)`
`or 0-veca.vecc=r(vecb.vecc)ort=-((veca.vecc)/(vecb.vecc))`
from (i) and (ii) solution of `vecr" is " vecr =veca-((veca.vecc)/(vecb.vecc))vecb`
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