Question

Find the equation of the plane passing through the following points.

 (2, 1, 0), (3, −2, −2) and (3, 1, 7)

Answer 1

 The equation of the plane passing through points (2, 1, 0), (3, −2, −2) and (3, 1, 7) is given by

\[\begin{vmatrix}x - 2 & y - 1 & z - 0 \\ 3 - 2 & - 2 - 1 & - 2 - 0 \\ 3 - 2 & 1 - 1 & 7 - 0\end{vmatrix} = 0\]

\[ \Rightarrow \begin{vmatrix}x - 2 & y - 1 & z - 0 \\ 1 & - 3 & - 2 \\ 1 & 0 & 7\end{vmatrix} = 0\]

\[ \Rightarrow - 21 \left( x - 2 \right) - 9 \left( y - 1 \right) + 3z = 0\]

\[ \Rightarrow - 21x + 42 - 9y + 9 + 3z = 0\]

\[ \Rightarrow - 21x - 9y + 3z + 51 = 0\]

\[ \Rightarrow 21x + 9y - 3z = 51\]

\[ \Rightarrow 7x + 3y - z = 17\]