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

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Presentation transcript:

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

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 The Cross ProductChapter 12

President UniversityErwin SitompulMVC 2/3 The Cross Product of Two Vectors in Space 12.4 The Cross ProductChapter 12

President UniversityErwin SitompulMVC 2/4 The Cross Product of Two Vectors in Space 12.4 The Cross ProductChapter 12

President UniversityErwin SitompulMVC 2/5 The Cross Product of Two Vectors in Space Chapter The Cross Product Example

President UniversityErwin SitompulMVC 2/6 |u  v| is the Area of a Parallelogram Chapter The Cross Product

President UniversityErwin SitompulMVC 2/7 Distance and Spheres in Space Example Chapter The Cross Product Example

President UniversityErwin SitompulMVC 2/8 Lines in Space Chapter 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.

President UniversityErwin SitompulMVC 2/9 Lines in Space Chapter Lines and Planes in Space

President UniversityErwin SitompulMVC 2/10 Lines in Space Chapter 12 Example 12.5 Lines and Planes in Space

President UniversityErwin SitompulMVC 2/11 Lines in Space Example Chapter Lines and Planes in Space What if we choose Q(1,–1,4) as the base?

President UniversityErwin SitompulMVC 2/12 The Distance from a Point to a Line in Space Chapter Lines and Planes in Space

President UniversityErwin SitompulMVC 2/13 The Distance from a Point to a Line in Space Chapter Lines and Planes in Space Example

President UniversityErwin SitompulMVC 2/14 The Distance from a Point to a Plane Chapter Lines and Planes in Space

President UniversityErwin SitompulMVC 2/15 The Distance from a Point to a Plane Chapter Lines and Planes in Space Example

President UniversityErwin SitompulMVC 2/16 Chapter 13 Vector-Valued Functions and Motion in Space

President UniversityErwin SitompulMVC 2/17 Vector Functions Chapter Vector Functions

President UniversityErwin SitompulMVC 2/18 Vector Functions Chapter Vector Functions Can you see the difference?

President UniversityErwin SitompulMVC 2/19 Vector Functions Chapter Vector Functions

President UniversityErwin SitompulMVC 2/20 Limits and Continuity Chapter Vector Functions

President UniversityErwin SitompulMVC 2/21 Limits and Continuity Chapter Vector Functions

President UniversityErwin SitompulMVC 2/22 Derivatives and Motion Chapter Vector Functions

President UniversityErwin SitompulMVC 2/23 Derivatives and Motion Chapter Vector Functions

President UniversityErwin SitompulMVC 2/24 Derivatives and Motion Chapter Vector Functions Example

President UniversityErwin SitompulMVC 2/25 Derivatives and Motion Chapter Vector Functions

President UniversityErwin SitompulMVC 2/26 Differentiation Rules Chapter Vector Functions

President UniversityErwin SitompulMVC 2/27 Vector Functions of Constant Length Chapter Vector Functions

President UniversityErwin SitompulMVC 2/28 Vector Functions of Constant Length Chapter Vector Functions Example

President UniversityErwin SitompulMVC 2/29 Integrals of Vector Functions Chapter Vector Functions Example

President UniversityErwin SitompulMVC 2/30 Integrals of Vector Functions Chapter Vector Functions Example

President UniversityErwin SitompulMVC 2/31 Integrals of Vector Functions Chapter Vector Functions Example

President UniversityErwin SitompulMVC 2/32 Integrals of Vector Functions Chapter Vector Functions

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 Vector Functions