MATH 1920 Lecture Notes - Lecture 4: Dot Product

• School: Cornell University
• Department: Mathematics
• Course: MATH 1920
• Professor: Andrew Sale

Document Summary

A normal vector to the plane (these values are not unique) Any points p and q in the plane will satisfy the equation: Let: p = (x0, y0, z0) - p is some arbitrary set point in the plane n = - n is the normal vector to the plane. Q = (x, y, z) - q is any point in the plane. The equation of the plane is: ax + by + cz = d where d = op n (op is the position vector of point p) Given the equation of a plane: ax + by + cz = d. The normal vector to the plane is n = Example: given p = (1, 1, 0), q = (0, 0, 2), and r = (1, 3, -1), find the equation of the plane containing p, q, and r. n = pq x pr. Pq x pr is normal to the plane.