# 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

Solution:

$\\ \\ \vec{a}=i-k\\ \\ \vec{b}=xi+j+(1-x)k\\ \\ c=yi+xj+(1+x-y)k\\ \\ \Rightarrow \hspace{1cm}=\begin{vmatrix} 1 &0 &-1 \\ x& 1 &1-x \\ y &x &1+x-y \end{vmatrix}\\ \\ \Rightarrow \hspace{1cm}1+x-y-x^{2}+y-x+x^{2}=1$

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