Download presentation
Presentation is loading. Please wait.
Published byMatthew McKenzie Modified over 9 years ago
1
Dr.-Ing. Erwin Sitompul President University Lecture 2 Multivariable Calculus President UniversityErwin SitompulMVC 2/1 http://zitompul.wordpress.com
2
President UniversityErwin SitompulMVC 2/2 The Cross Product of Two Vectors in Space In space, we need a way to describe how a plane is tilting. We accomplish this by multiplying two vectors in the plane together to get a third vector perpendicular to the plane The direction of this third vector tells us the “inclination” of the plane. We use cross product to multiply the vectors together. 12.4 The Cross ProductChapter 12
3
President UniversityErwin SitompulMVC 2/3 The Cross Product of Two Vectors in Space 12.4 The Cross ProductChapter 12
4
President UniversityErwin SitompulMVC 2/4 The Cross Product of Two Vectors in Space 12.4 The Cross ProductChapter 12
5
President UniversityErwin SitompulMVC 2/5 The Cross Product of Two Vectors in Space Chapter 1212.4 The Cross Product Example
6
President UniversityErwin SitompulMVC 2/6 |u v| is the Area of a Parallelogram Chapter 1212.4 The Cross Product
7
President UniversityErwin SitompulMVC 2/7 Distance and Spheres in Space Example Chapter 1212.4 The Cross Product Example
8
President UniversityErwin SitompulMVC 2/8 Lines in Space Chapter 1212.5 Lines and Planes in Space Suppose L is a line in space passing through a point P 0 (x 0,y 0,z 0 ) parallel to a vector v. Then L is the set of all points P(x,y,z) for which P 0 P is parallel to v. P 0 P = tv, for a given value of scalar parameter t.
9
President UniversityErwin SitompulMVC 2/9 Lines in Space Chapter 1212.5 Lines and Planes in Space
10
President UniversityErwin SitompulMVC 2/10 Lines in Space Chapter 12 Example 12.5 Lines and Planes in Space
11
President UniversityErwin SitompulMVC 2/11 Lines in Space Example Chapter 1212.5 Lines and Planes in Space What if we choose Q(1,–1,4) as the base?
12
President UniversityErwin SitompulMVC 2/12 The Distance from a Point to a Line in Space Chapter 1212.5 Lines and Planes in Space
13
President UniversityErwin SitompulMVC 2/13 The Distance from a Point to a Line in Space Chapter 1212.5 Lines and Planes in Space Example
14
President UniversityErwin SitompulMVC 2/14 The Distance from a Point to a Plane Chapter 1212.5 Lines and Planes in Space
15
President UniversityErwin SitompulMVC 2/15 The Distance from a Point to a Plane Chapter 1212.5 Lines and Planes in Space Example
16
President UniversityErwin SitompulMVC 2/16 Chapter 13 Vector-Valued Functions and Motion in Space
17
President UniversityErwin SitompulMVC 2/17 Vector Functions Chapter 1313.1 Vector Functions
18
President UniversityErwin SitompulMVC 2/18 Vector Functions Chapter 1313.1 Vector Functions Can you see the difference?
19
President UniversityErwin SitompulMVC 2/19 Vector Functions Chapter 1313.1 Vector Functions
20
President UniversityErwin SitompulMVC 2/20 Limits and Continuity Chapter 1313.1 Vector Functions
21
President UniversityErwin SitompulMVC 2/21 Limits and Continuity Chapter 1313.1 Vector Functions
22
President UniversityErwin SitompulMVC 2/22 Derivatives and Motion Chapter 1313.1 Vector Functions
23
President UniversityErwin SitompulMVC 2/23 Derivatives and Motion Chapter 1313.1 Vector Functions
24
President UniversityErwin SitompulMVC 2/24 Derivatives and Motion Chapter 1313.1 Vector Functions Example
25
President UniversityErwin SitompulMVC 2/25 Derivatives and Motion Chapter 1313.1 Vector Functions
26
President UniversityErwin SitompulMVC 2/26 Differentiation Rules Chapter 1313.1 Vector Functions
27
President UniversityErwin SitompulMVC 2/27 Vector Functions of Constant Length Chapter 1313.1 Vector Functions
28
President UniversityErwin SitompulMVC 2/28 Vector Functions of Constant Length Chapter 1313.1 Vector Functions Example
29
President UniversityErwin SitompulMVC 2/29 Integrals of Vector Functions Chapter 1313.1 Vector Functions Example
30
President UniversityErwin SitompulMVC 2/30 Integrals of Vector Functions Chapter 1313.1 Vector Functions Example
31
President UniversityErwin SitompulMVC 2/31 Integrals of Vector Functions Chapter 1313.1 Vector Functions Example
32
President UniversityErwin SitompulMVC 2/32 Integrals of Vector Functions Chapter 1313.1 Vector Functions
33
President UniversityErwin SitompulMVC 2/33 Homework 2 Chapter 13 Exercise 12.4, No. 15. Exercise 12.4, No. 36. Exercise 12.5, No. 6. Exercise 12.5, No. 43. Exercise 13.1, No. 7. Exercise 13.1, No. 25. Due: Next week, at 17.15. 13.1 Vector Functions
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.