Find the equation of the plane through points (2,1,0),(3,-2,-2), and (3,1,7).

Explanation

To find the equation of the plane passing through the points \( A(2, 1, 0) \), \( B(3, -2, -2) \), and \( C(3, 1, 7) \), we can use the determinant method. The equation of the plane can be expressed as:

\[
\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
...