Michigan State University
Math 234 – Spring 2024
Lecture 05

January 19, 2024

Key takeaways:

  • Equation of plane, normal vector of a plane, how to find a plane knowing 3 points.

  • Angle between two planes

  • Distance of a point to a plane

1 Equation of plane

If n=(a,b,c) is a given vector, r0=(x0,y0,z0) is the position vector for P0(x0,y0,z0), then the plane going through (P) going through P0 and is perpendicular to n is given by

  • Vector form r=(x,y,z)(P) if

    n(rr0)=0
  • Parametric form r=(x,y,z)(P) if

    n(rr0)=0a(xx0)+b(yy0)+c(zz0)=0
  • Other parametric form sometime we write

    ax+by+cz(ax0+by0+cz0)d=0,orax+by+cz=d.

2 Distance from a point to a plane

Theorem 1
d=|RP0n||n|