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vecalpha and vecbeta are two unit vectos...

`vecalpha` and `vecbeta` are two unit vectos and `vecr` is a vector such that `vecr,vecalpha=0` and `sqrt(2)(vecrxxvecbeta)=3(vecrxxvecalpha)-vecbeta`, then `(1)/(|vecr|^(2))` equal

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The correct Answer is:
7
`vecr.hatbeta=0` (taking dot on both the sides of the given equation and using `vecr.vecalpha=0`)
`sqrt(2)vecrxx(vecrxxhatbeta)=3vecrxx(vecrxxhatalpha)-vecrxxhatbeta`
`impliessqrt(2)((vecr.hatbeta)vecr-(vecr.vecr)hatbeta)=3((vecr.hatalpha)-vecrxxhatbeta`
`sqrt(2)((vecr.hatbeta)vecr-(vecr.vecr)hatbeta)=3((vecr.hatalpha)vecr-(vecr.vecr)hatalpha)-vecrxxhatbeta`
`implies-sqrt(2)|vecr|^(2)hatbeta=-3|vecr|^(2)hatalpha-vecrxxhatbeta`
`implies3|vecr|^(2)hatalpha=-vecrxxhatbeta+sqrt(2)|vecr|^(2)hatbeta`
`implies9|vecr|^(4)=|vecr|^(2)+2|vecr|^(4)`
`implies|vecr|=(1)/(sqrt(7))`
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