A plane is specified as $(x, y, z)=(0, 1, 1)+\lambda(1, -1, 1)+\mu(2, -1,0)$, and I'm supposed to find the plane equation. Using the formula \begin{equation} \begin{vmatrix} x-x_1 & y-y_1 & z-z_1\\ x_2-x_1 & y_2-y_1 & z_2-z_1\\ x_3-x_1 & y_3-y_1 & z_3-z_1\\ \end{vmatrix} =0 \end{equation} should have been simple enough, but what I keep getting, (considering points 1, 2, and 3 as per the order in which they're specified in the plane equation); \begin{equation} \begin{vmatrix} x & y-1 & z-1\\ 1 & -2 & 0\\ 2 & -2 & -1\\ \end{vmatrix} =0 \end{equation} while the correct answer is this; \begin{equation} \begin{vmatrix} x & y-1 & z-1\\ 1 & -1 & 1\\ 2 & -1 & 0\\ \end{vmatrix} =0 \end{equation}
Can someone help me with where I went wrong?