Find the equation of the plane formed by the points (2, -1, 0), (0, 2, 3) and (1, -2, -1)

Concept:

The equation of the plane formed by the points (x₁, y₁, z₁), (x₂, y₂, z₂) and (x₃, y₃, z₃) is

\(\rm \begin{vmatrix} x -x_1 & y- y_1 &z - z_1 \\ x_2-x_1& y_2- y_1 & z_2 - z_1 \\ x_3-x_1& y_3- y_1 & z_3 - z_1 \end{vmatrix} = 0\)

Calculation:

The given points are (2, -1, 0), (0, 2, 3) and (1, -2, -1)

The equation of the plane will be 

\(\rm \begin{vmatrix} x -2 & y- (-1) &z - 0\\ 0-2& 2- (-1)& 3- 0\\ 1-2& -2- (-1)& -1- 0 \end{vmatrix} = 0\)

⇒ \(\rm \begin{vmatrix} x -2 & y+1 &z\\ -2& 3& 3\\ -1& -1& -1 \end{vmatrix} = 0\)

⇒(x - 2)(-3-(-3)) - (y + 1)(2 + 3) + z(2 + 3) = 0

⇒ -5y - 5 + 5z = 0

⇒ y - z + 1 = 0