MATH 1920 Lecture Notes - Lecture 2: Dot Product

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

Document Summary

Lecture 2 - 3d surfaces and dot products. Let q be the center of a sphere s with radius r. Then s consists of all points x, y, z such that: (x - a)2 + (y - b)2 + (z - c)2 = r2. The z coordinates are not specified because they can take any value (unless otherwise specified) Lines: to describe a line you need a direction vector and a point on the line v = l. L(t) = (x0, y0, z0) + t where t (the parameter) is any real number. Vector parametric equations: x(t) = x0 + ta y(t) = y0 + tb z(t) = z0 + tc. What information do we need to describe a plane in 3. Definition of dot product: when v = and u = , v u = v1u1 + v2u2 + v3u3.