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Question
Find the equation of the plane passing through the following point
(0, −1, 0), (3, 3, 0) and (1, 1, 1)
Solution
The equation of the plane passing through points (0, −1, 0), (3, 3, 0) and (1, 1, 1) is given by
\[\begin{vmatrix}x - 0 & y + 1 & z - 0 \\ 3 - 0 & 3 + 1 & 0 - 0 \\ 1 - 0 & 1 + 1 & 1 - 0\end{vmatrix} = 0\]
\[ \Rightarrow \begin{vmatrix}x - 0 & y + 1 & z - 0 \\ 3 & 4 & 0 \\ 1 & 2 & 1\end{vmatrix} = 0\]
\[ \Rightarrow 4x - 3 \left( y + 1 \right) + 2z = 0\]
\[ \Rightarrow 4x - 3y + 2z = 3\]
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