Let vector a = i-k , vector b =xi+j+(1-x)k and vector c=yi+xj+(1+x-y) k Then vector a , b and c are non- coplanar for

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         \ \ veca=i-k\ \ vecb=xi+j+(1-x)k\ \ c=yi+xj+(1+x-y)k\ \ Rightarrow hspace1cm=eginvmatrix 1 &0 &-1 \ x& 1 &1-x \ y &x &1+x-y endvmatrix\ \ Rightarrow hspace1cm1+x-y-x^2+y-x+x^2=1  

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