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Question
Write the equation of the plane passing through points (a, 0, 0), (0, b, 0) and (0, 0, c).
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Solution
The equation of the plane passing through (a, 0, 0), (0, b, 0) and (0, 0, c) is
\[\begin{vmatrix}x - a & y - 0 & z - 0 \\ 0 - a & b - 0 & 0 - 0 \\ 0 - a & 0 - 0 & c - 0\end{vmatrix} = 0 \]
\[ \Rightarrow \begin{vmatrix}x - a & y & z \\ - a & b & 0 \\ - a & 0 & c\end{vmatrix} = 0\]
\[ \Rightarrow bc \left( x - a \right) + acy + abz = 0\]
\[ \Rightarrow bcx + acy + abz = abc\]
\[\text{ Dividing the equation by abc, we get
} \]
\[\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1\]
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