MATH115 Lecture Notes - Lecture 3: Dissociation Constant, Hyperplane
10 Oct 2015
School
Department
Course
Professor
Document Summary
In this lecture we discuss two equations containing vectors which represent a plane in 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 this 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. This holds true for all vectors x on the plane p. Hence the vectors on p are precisely those vectors x that satisfy x a is orthogonal to n. Thus for any point x on p,
