MATH136 Lecture Notes - Hyperplane

• School: University of Waterloo
• Department: Mathematics
• Course: MATH136
• Professor: Robert Andre

Document Summary

Friday, january 17 (cid:16) lecture 6 : planes in (cid:1337)3: plane n (cid:152) (x (cid:16) a) = 0 in (cid:1337)3 where n is a norm to the plane, hyperplane in (cid:1337)n. In this lecture we discuss two equations containing vectors which represent a plane in (cid:1337)3. We will assume an intuitive understanding of a plane in 3-space. We want to formulate a mathematical representation of a plane p in 3-space in such a way that mathematical representation corresponds to our intuitive perception of what the set of points (vectors) in p are. Given a plane p we can imagine a vector n = (n1, n2, n3) whose directed line segment is perpendicular (orthogonal) to all line segments which lie on p. Say a = (a1, a2, a3) is any point (vector) on p. We want to find a way to recognize all points (vectors) x which are on p.