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(C) The equation of a plane passing through three non-collinear points $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,and $(x_3, y_3, z_3)$ is given by the deter

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$7x - 9y - z - 5 = 0$

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(C) The equation of a plane passing through three non-collinear points $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,and $(x_3, y_3, z_3)$ is given by the determinant equation: $\begin{vmatrix} x-x_1 & y-y_1 & z-z_1 \ x_2-x_1 & y_2-y_1 & z_2-z_1 \ x_3-x_1 & y_3-y_1 & z_3-z_1 \end{vmatrix} = 0$ Substituting the given points $(2,1,0)$,$(3,2,-2)$,and $(3,1,7)$: $\begin{vmatrix} x-2 & y-1 & z-0 \ 3-2 & 2-1 & -2-0 \ 3-2 & 1-1 & 7-0 \end{vmatrix} = 0$ $\begin{vmatrix} x-2 & y-1 & z \ 1 & 1 & -2 \ 1 & 0 & 7 \end{vmatrix} = 0$ Expanding along the first row: $(x-2)(7 - 0) - (y-1)(7 - (-2)) + z(0 - 1) = 0$ $(x-2)(7) - (y-1)(9) - z = 0$ $7x - 14 - 9y + 9 - z = 0$ $7x - 9y - z - 5 = 0$

The equation of the plane passing through the points $(2,1,0)$,$(3,2,-2)$,and $(3,1,7)$ is

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