Mathematics - Vector Question with Solution | TestHub

Here, $[abc]=|a\cdot (b\times c)|$ Now, according to question, $\begin{array}{rl}\left[\begin{array}{ll}a& bc\end{array}\right]& =\left|\begin{array}{ccc}1& 0& -1\\ x& 1& 1-x\\ y& x& 1+x-y\end{array}\right|\\ & =1(1+x-y-x(1-x))-1\left(x^2-y\right)\\ & =1+x-y-x+x^2-x^2+y\\ & =1\\ & =\text{ Independent of }x\text{ and }y.\end{array}$