This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 241 Chapter 11 Dr. Justin O. WyssGallifent § 11.1 Cartesian Coordinates in Space 1. Preliminaries: How to plot points in 3space, the coordinate planes, the first octant. Emphasize how perspective can be confusing at first. 2. Distance between points:  PQ  = radicalbig ( x 1 − x ) 2 + ( y 1 − y ) 2 + ( z 1 − z ) 2 3. Equation of a circle, a closed disk, a sphere and a closed ball. Pictures of all. § 11.2 Vectors in Space 1. Definition of a vector as a triple of numbers. The notation ¯ a or → a . We can add and subtract vectors by adding and subtracting components and we can multiply a scalar by a vector by multiplying by all the components. Three special vectors are ˆ ı = (1 , , 0), ˆ = (0 , 1 , 0) and ˆ k = (0 , , 1). Then every vector can be written as ¯ a = a 1 ˆ ı + a 2 ˆ + a 3 ˆ k . Vectors are not necessarily anchored anywhere though often we anchor them somewhere (the origin, for example) for some reason. 2. Basic properties and associated definitions: (a) The zero vector is ¯ 0 = 0ˆ ı + 0 ˆ + 0 ˆ k ....
View
Full
Document
This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff
 Math

Click to edit the document details