Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Given that lines are coplanar. $\therefore \left|\begin{array}{ccc}{x}_2-x_1& y_2-y_1& z_2-z_1\\ a_1& b_1& c_1\\ a_2& b_2& c_2\end{array}\right|=\left|\begin{array}{ccc}2& 0& 0\\ 2& k& 2\\ 5& 2& k\end{array}\right|=0\Rightarrow k=\pm 2$ For $k=2$, equation of the plane is given by $\left|\begin{array}{ccc}x-1& y+1& z\\ 2& 2& 2\\ 5& 2& 2\end{array}\right|=0\Rightarrow y-z+1=0$ For $k=-2$, equation of the plane is given by $\left|\begin{array}{ccc}x-1& y+1& z\\ 2& -2& 2\\ 5& 2& -2\end{array}\right|=0\Rightarrow y+z+1=0$