Chapter 6 - Chapter Chapter 6 Three Dimensional Space...

Info iconThis preview shows pages 1–18. Sign up to view the full content.

View Full Document Right Arrow Icon
hapter 6 Chapter 6 Three Dimensional Space
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Overview he Cartesian Coordinate System The Cartesian Coordinate System ectors Vectors Definitions l b t 2 t Angle between 2 vectors Scalar or Dot Product roperties of Scalar Product Properties of Scalar Product
Background image of page 2
Overview nit Vectors Unit Vectors Projection Vector Product roperties of Vector Product Properties of Vector Product ines in 3 Space Lines in 3-D Space Vector Equation of a Line arametric Equation of a Line Parametric Equation of a Line
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Overview lanes Planes Equation for Plane istance from Point to Plane Distance from Point to Plane ector Functions of One Variable Vector Functions of One Variable Limits and Continuity erivatives of Vector Functions Derivatives of Vector Functions Definite Integral of a Vector Function
Background image of page 4
Overview pace Curves Space Curves Smooth Curves angent Vector and Line to a Curve Tangent Vector and Line to a Curve Arc Length of a Space Curve
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
he Cartesian Coordinate The Cartesian Coordinate System
Background image of page 6
The Cartesian Coordinate System ectangular Coordinates Rectangular Coordinates c z (,,) Pabc Right-handed coordinates system b y 0 a x If we rotate the axis counterclockwise toward the axis, xy  then a right-handed screw will move in the positive direction. z
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Cartesian Coordinate System 0 , 0 , 0 : Planes z y x z Eight Octants 0 y 0 z 0 x x y
Background image of page 8
The Cartesian Coordinate System istane between two points Distane between two points z 2222 (, , ) Px y z 111 , ) y z 1111 y 0 x 2 1 2 2 1 2 2 1 2 2 1 ) ( ) ( ) ( z z y y x x P P
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Cartesian Coordinate System 00 Equation of circle of radius and center ( , ) rx y x r ) y ( , xy 2 2 0 y 22 Equation of circle: () ( ) x x yy r 
Background image of page 10
The Cartesian Coordinate System 00 0 Equation of the sphere of radius and center ( , , ) rx y z z r ) yz 0 000 ( ,, xyz x y 2 2 0 2 0 2 0 ) ( ) ( ) ( : sphere of Equation r z z y y x x
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Vectors
Background image of page 12
Vectors – Definitions directed line segment PQ A directed line segment PQ Q (terminal point) (initial point) P Direction: Magnitude: direction of the arrow length of the line segment Two vectors are equal if they have the same direction and length. qy g =
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Vectors – Definitions he vector of ( ) : x yz osition 0 x   00 0 The ,, ) : Px position 0 0 OP y z   The of is denoted by : OP length 22 2 0 || || OP x y z  () magnitude z 0 0 (, , ) Px y z . 0 0 is vector The 0 zero 0 x y
Background image of page 14
Vectors – Definitions 2 x Addition 1 1 1 y x v 2 2 2 z y v 1 z 1 v 2 1 2 1 2 1 y y x x v v 2 v 2 1 z z
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Vectors – Definitions 2 x Addition 1 1 1 y x v 2 2 2 z y v 1 z 2 v 1 v 2 1 2 1 2 1 y y x x v v 2 1 z z
Background image of page 16
Vectors – Definitions Negative
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 18
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/01/2011 for the course MATH 1505 taught by Professor Yap during the Spring '11 term at National University of Singapore.

Page1 / 115

Chapter 6 - Chapter Chapter 6 Three Dimensional Space...

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online