Question

Find the equation of the plane through $(2,1,3)$ making equal intercepts on X and Y-axis and intercepts 4 on Z-axis.

Answer 1

Let the equation of plane be

$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

since it has equal intercepts $a=b=c$

we have

$x+y+z=a$

$a=2+1+3=6$

$\therefore x+y+z=6$ is the required equation.