MATH125 Lecture Notes - Lecture 7: Hyperplane

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: George Peschke

Document Summary

Let h be the hyperspace of all x ^n with a (x - p) = 0 p, a , a != 0. Then, the distance of a point q, with position vector q, from h is dist(q,h) = |a (q - p)|(1/||a||) = ||proj_a(q - p)|| The point on h which is closest to q is r with the position vector r = q - (a (q - p) / (a a)) a = q - proj_a(q - p) Find the distance of the point q(3,3,3) from the hyperplane h x + 2y + z = 1. Need: some normal vector to the hyperplane a = (1, 2, 1) P = (1, 0, 0) proj_a(q - p) = ((a (q - p)) / (a a)) a. = (11/6)(1, 2, 1) dist(q, h) = ||(11/6)(1,2,1)|| R has position vector y = q - proj_a(q - p)