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`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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Answer» Correct Answer - 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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