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Question
Find the equation of the plane passing through the following points.
(2, 1, 0), (3, −2, −2) and (3, 1, 7)
Solution
The equation of the plane passing through points (2, 1, 0), (3, −2, −2) and (3, 1, 7) is given by
\[\begin{vmatrix}x - 2 & y - 1 & z - 0 \\ 3 - 2 & - 2 - 1 & - 2 - 0 \\ 3 - 2 & 1 - 1 & 7 - 0\end{vmatrix} = 0\]
\[ \Rightarrow \begin{vmatrix}x - 2 & y - 1 & z - 0 \\ 1 & - 3 & - 2 \\ 1 & 0 & 7\end{vmatrix} = 0\]
\[ \Rightarrow - 21 \left( x - 2 \right) - 9 \left( y - 1 \right) + 3z = 0\]
\[ \Rightarrow - 21x + 42 - 9y + 9 + 3z = 0\]
\[ \Rightarrow - 21x - 9y + 3z + 51 = 0\]
\[ \Rightarrow 21x + 9y - 3z = 51\]
\[ \Rightarrow 7x + 3y - z = 17\]
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