The equation of a plane passing through $(-1,2,3)$ and whose normal makes equal angles with the coordinate axes is

Since, normal makes equal angles with co-ordinate axis. So, it intercept with all the axis will be same. So, equation of plane will be : $$ \frac{x}{a}+\frac{y}{a}+\frac{z}{a}=1 \Rightarrow x+y+z=a.....(i) $$ Now, it passes through $(-1,2,3)$. So, we get $$ -1+2+3=a \Rightarrow a=4 $$ Putting the values of a in equation (i), we get $$ x+y+z-4=0 $$