Question

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

Answer 1

The equation of the plane passing through (a, 0, 0), (0, b, 0) and (0, 0, c) is
$$\begin{gathered} \left|\begin{array}{ccc}x-a& y-0& z-0\\ 0-a& b-0& 0-0\\ 0-a& 0-0& c-0\end{array}\right|=0 \\ \Rightarrow \left|\begin{array}{ccc}x-a& y& z\\ -a& b& 0\\ -a& 0& c\end{array}\right|=0 \\ \Rightarrow bc\left(x-a\right)+acy+abz=0 \\ \Rightarrow bcx+acy+abz=abc \\ \text{Dividing the equation by}\mathit{\text{abc}}\text{, we get} \\ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 \end{gathered}$$