Using an equation in intercepts, write an implicit equation of the plane which intersects the Cartesian coordinate axes X, Y and Z at the three points with coordinates P1=(2, 0, 0), P2=(0, 4, 0) and P3=(0, 0, 6), respectively.
I am having a hard time visualizing this. Can someone help me?
This is a well-known formula, similar to the formula for the equation of a line in a plane, given its intercepts:
If the $x$-intercept of the plane is $(a,0,0)$, its $y$-intercept $(0,b,0)$ and its $z$-intercept $(0,0,c)$ $(a,b, c\ne 0)$, the equation of the plane is $$\frac xa+\frac yb+\frac zc=1.$$