MHB What is the Maximum Inclination of a 3D Plane and its Equation in the XY Plane?

[cptolemy]

Hi,

If I have a 3D plane Ax+By+Cz=0, and I know the line equation of its intersection with the reference plane, what is the maximum inclination a point can have and what is its equation in the xy plane?

Is it perpendicular to the intersection? That is , if the slope of the intersection line is m, the max will be given by the line with a slope of -1/m?

This is embarassing...

Cheers,

Kepler

 

[HallsofIvy]

If I understand what you mean by "inclination" then, yes, the plane with maximum "inclination" to a given plane is perpendicular to it. And, yes, if a line is perpendicular to a line with (non-zero) slope m, then it has slope -1/m. Note that if m= 0, so "horizontal", then the perpendicular line is "vertical" and does not have a defined slope.