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प्रश्न
Write the equation of the plane passing through points (a, 0, 0), (0, b, 0) and (0, 0, c).
उत्तर
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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