MATH136 Lecture Notes - Lecture 6: Hyperplane
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MATH136 Full Course Notes
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Friday, january 17 lecture 6 : planes in 3: plane n (x a) = 0 in 3 where n is a norm to the plane, hyperplane in n. 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 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. This holds true for all vectors x on the plane p.
