Question

Find the equation of the plane passing through the point (2, 4, 6) and making equal intercepts on the coordinate axes.

Answer 1

$$\begin{gathered} \text{We know that the equation of the plane whose intercepts on the coordianate axes are}\mathit{\text{a}}\text{,}\mathit{\text{b}}\text{and}\mathit{\text{c}}\text{is} \\ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1 \\ \text{Given that the plane makes equal intercepts on the coordiante axes.} \\ \text{So,}a=b=c \\ \text{So, the equation of the plane is} \\ \frac{x}{a}+\frac{y}{a}+\frac{z}{a}=1 \\ \Rightarrow x+y+z=a...\left(1\right) \\ \text{This plane passes through the point (2, 4, 6).} \\ \text{Substituting this point in (1), we get} \\ 2+4+6=a \\ \Rightarrow a=12 \\ \text{Substituting this in (1), we get} \\ x+y+z=12 \end{gathered}$$