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Dr.-Ing. Erwin Sitompul President University Lecture 2 Multivariable Calculus President UniversityErwin SitompulMVC 2/1

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Presentation on theme: "Dr.-Ing. Erwin Sitompul President University Lecture 2 Multivariable Calculus President UniversityErwin SitompulMVC 2/1"— Presentation transcript:

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

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