Vector Products (Cross Product)

Slides:



Advertisements
Similar presentations
11.4 The Cross product For an animation of this topic visit:
Advertisements

12 VECTORS AND THE GEOMETRY OF SPACE.
10.4 Cross product: a vector orthogonal to two given vectors Cross product of two vectors in space (area of parallelogram) Triple Scalar product (volume.
Chapter 12 – Vectors and the Geometry of Space 12.4 The Cross Product 1.
Vectors in Two and Three Dimensions. Definition A vector is a quantity that is determined by a magnitude and a direction.
The Vector or Cross Product Lecture V1.3 Example 5 Moodle.
Vector Products (Cross Product). Torque F r T F r T F1F1 F2F2.
Lecture 13 Today Basic Laws of Vector Algebra Scalars: e.g. 2 gallons, $1,000, 35ºC Vectors: e.g. velocity: 35mph heading south 3N force toward.
Analytic Geometry in Three Dimensions
Vectors in the Plane and in Three-Dimensional Space.
Lecture 1eee3401 Chapter 2. Vector Analysis 2-2, 2-3, Vector Algebra (pp ) Scalar: has only magnitude (time, mass, distance) A,B Vector: has both.
Vector Torque. Direction of Angular Velocity  Angular velocity can be clockwise or counterclockwise around the axis of rotation.  It has magnitude and.
Vector Product Results in a vector.
Cross Product Ali Tamaki Ben Waters Linear Systems Spring 2006.
The Cross Product of 2 Vectors 11.3 JMerrill, 2010.
11 Analytic Geometry in Three Dimensions
The Cross Product of Two Vectors In Space Section
Five-Minute Check (over Lesson 8-4) Then/Now New Vocabulary
Vectors and the Geometry of Space Copyright © Cengage Learning. All rights reserved.
The Cross Product Third Type of Multiplying Vectors.
Section 13.4 The Cross Product.
Torque The magnitude of the torque depends on two things: The distance from the axis of the bolt to the point where the force is applied. This is |r|,
Section 9.4: The Cross Product Practice HW from Stewart Textbook (not to hand in) p. 664 # 1, 7-17.
Vectors and the Geometry of Space 11 Copyright © Cengage Learning. All rights reserved.
Elementary Linear Algebra Howard Anton Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 3.
1 Chapter 14 Introduction to Spatial Vector Analysis The term vector has slightly different meanings in different areas of mathematics, engineering and.
7.1 Scalars and vectors Scalar: a quantity specified by its magnitude, for example: temperature, time, mass, and density Chapter 7 Vector algebra Vector:
VECTOR CALCULUS. Vector Multiplication b sin   A = a  b Area of the parallelogram formed by a and b.
Section 13.4 The Cross Product. Torque Torque is a measure of how much a force acting on an object causes that object to rotate –The object rotates around.
1. Vector Analysis 1.1 Vector Algebra Vector operations A scalar has a magnitude (mass, time, temperature, charge). A vector has a magnitude (its.
Properties of Vector Operations: u, v, w are vectors. a, b are scalars. 0 is the zero vector. 0 is a scalar zero. 1. u + v = v + u 2. (u + v) + w = u +
Vectors CHAPTER 7. Ch7_2 Contents  7.1 Vectors in 2-Space 7.1 Vectors in 2-Space  7.2 Vectors in 3-Space 7.2 Vectors in 3-Space  7.3 Dot Product 7.3.
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Chapter 12: Vectors Cartesian.
Vector Products (Cross Product). Torque F r T.
Copyright © Cengage Learning. All rights reserved. 12 Vectors and the Geometry of Space.
Copyright © Cengage Learning. All rights reserved.
Section 11.4 The Cross Product Calculus III September 22, 2009 Berkley High School.
1. Determine vectors and scalars from these following quantities: weight, specific heat, density, volume, speed, calories, momentum, energy, distance.
Sec 13.3The Dot Product Definition: The dot product is sometimes called the scalar product or the inner product of two vectors.
Vectors and the Geometry
Mathematics. Session Vectors -2 Session Objectives  Vector (or Cross) Product  Geometrical Representation  Properties of Vector Product  Vector Product.
VECTORS AND THE GEOMETRY OF SPACE. The Cross Product In this section, we will learn about: Cross products of vectors and their applications. VECTORS AND.
Copyright © Cengage Learning. All rights reserved. 11 Analytic Geometry in Three Dimensions.
Lesson 87: The Cross Product of Vectors IBHL - SANTOWSKI.
Specialist Mathematics Vectors and Geometry Week 3.
The Cross Product. We have two ways to multiply two vectors. One way is the scalar or dot product. The other way is called the vector product or cross.
EXAMPLE FORMULA DEFINITION 1.
CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.
Application of Vector product
The Cross Product: Objectives
Section 3.4 Cross Product.
Elementary Linear Algebra
ES2501: Statics/Unit 9-1: Moment of Force (3D cases)
Contents 7.1 Vectors in 2-Space 7.2 Vectors in 3-Space 7.3 Dot Product
Approximate Running Time is 29 Minutes
Vectors and Scalars Chapter 2.
Math 200 Week 2 - Monday Cross Product.
Vector Calculus – Part 1 By Dr. Samer Awad
By the end of Week 2: You would learn how to plot equations in 2 variables in 3-space and how to describe and manipulate with vectors. These are just.
C H A P T E R 3 Vectors in 2-Space and 3-Space
Lesson 81: The Cross Product of Vectors
Vectors and the Geometry
The Cross Product.
Mathematics.
11 Vectors and the Geometry of Space
Find the cross product {image} . {image} .
Dots and Cross Products of Vectors in Space
11.1 Even Answers.
Find the cross product {image} . {image} .
CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.
Presentation transcript:

Vector Products (Cross Product)

Torque T r F

Torque T r F1 F F2

Torque T r F1 F F2 ||T|| = ||F1||x ||r||

Torque T r F1 q F q F2 ||T|| = ||F1||x ||r|| = ||F|| x ||r|| sin q

Vector Products

Definition of Cross Product

Interpretation of the Cross Product a x b b a

Applications of the Cross Product Constructing Orthogonal Vectors Area of a Triangle or a Parallelogram Volume of a Parallelepiped Moment of Force Angular Velocity

Cross Product of Unit Vectors z k j y i x

Properties of the Cross Product

Cautions

Coordinate Formula

Application

Scalar Triple Product

Application