Find the cross product {image} . {image} .

Slides:



Advertisements
Similar presentations
Torque and Rotation.
Advertisements

The Cross Product of Two Vectors In Space
Torque and Rotation Physics.
Vector Multiplication: The Cross Product
Lecture 13: Force System Resultants
Physics 7C lecture 12 Torque Thursday November 7, 8:00 AM – 9:20 AM
Forces and Moments MET 2214 Ok. Lets get started.
12 VECTORS AND THE GEOMETRY OF SPACE.
Vectors and the Geometry of Space 9. The Cross Product 9.4.
Mechanical Force Notes
Chapter 12 – Vectors and the Geometry of Space 12.4 The Cross Product 1.
READING QUIZ The moment of a force about a specified axis can be determined using ___. A) a scalar analysis only B) a vector analysis only C) either a.
1. A unit vector is A) without dimensions. B) without direction. C) without magnitude. D) None of the above. 2. The force F = (3 i + 4 j ) N has a magnitude.
Vector Products (Cross Product). Torque F r T F r T F1F1 F2F2.
Vectors in the Plane Peter Paliwoda.
Five-Minute Check (over Lesson 8-4) Then/Now New Vocabulary
Vectors and the Geometry of Space Copyright © Cengage Learning. All rights reserved.
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|,
MOMENT ABOUT AN AXIS In-Class Activities: Check Homework Reading Quiz Applications Scalar Analysis Vector Analysis Concept Quiz Group Problem Solving Attention.
Vectors and the Geometry of Space 11 Copyright © Cengage Learning. All rights reserved.
7.1 Scalars and vectors Scalar: a quantity specified by its magnitude, for example: temperature, time, mass, and density Chapter 7 Vector algebra Vector:
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.
Bellringer Compare and explain in complete sentences and formulas how using the Newton’s three laws of motion find the resultant force.
Section 9.1 Polar Coordinates. x OriginPole Polar axis.
Assigned work: pg. 443 #2,3ac,5,6-9,10ae,11,12 Recall: We have used a direction vector that was parallel to the line to find an equation. Now we will use.
Equations of Lines and Planes
Section 11.4 The Cross Product Calculus III September 22, 2009 Berkley High School.
MOMENT ABOUT AN AXIS Today’s Objectives:
A 19-kg block on a rough horizontal surface is attached to a light spring (force constant = 3.0 kN/m). The block is pulled 6.3 cm to the right from.
DOT PRODUCT CROSS PRODUCT APPLICATIONS
8.4 Vectors. A vector is a quantity that has both magnitude and direction. Vectors in the plane can be represented by arrows. The length of the arrow.
Vectors and the Geometry
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.
Lesson 87: The Cross Product of Vectors IBHL - SANTOWSKI.
Torque  If an unbalanced force acts on an object at rest, and: 1)the force does not act along the center of mass of the object, 2)the object is fixed.
Cross product Torque Relationship between torque and angular acceleration Problem solving Lecture 21: Torque.
Extended Work on 3D Lines and Planes. Intersection of a Line and a Plane Find the point of intersection between the line and the plane Answer: (2, -3,
CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.
Dot Product of Vectors.
Forces and Moments Mo = F x d What is a moment?
The Cross Product: Objectives
Scalars & Vectors – Learning Outcomes
MOMENT ABOUT AN AXIS (Section 4.5)
MOMENT ABOUT AN AXIS Today’s Objectives:
MOMENT ABOUT AN AXIS (Section 4.5)
MOMENT ABOUT AN AXIS Today’s Objectives:
Q Terminal Point Initial Point P Directed line segment.
Chapter 3 VECTORS.
VECTORS APPLICATIONS NHAA/IMK/UNIMAP.
Engineering Mechanics : STATICS
Find a vector equation for the line through the points {image} and {image} {image}
Find a vector equation for the line through the points {image} and {image} {image}
Lesson 81: The Cross Product of Vectors
Find the curl of the vector field. {image}
Find {image} and the angle between u and v to the nearest degree: u = < 7, -7 > and v = < -8, -9 > Select the correct answer: 1. {image}
Find {image} , if {image} and {image} .
Vector Products (Cross Product)
Vectors and the Geometry
11 Vectors and the Geometry of Space
Understanding Torque Torque is a twist or turn that tends to produce rotation. * * * Applications are found in many common tools around the home or industry.
Find {image} , if {image} and {image} .
Evaluate the limit: {image} Choose the correct answer from the following:
Dots and Cross Products of Vectors in Space
Differentiate the function:   {image}
8.4 Vectors.
Find the cross product {image} . {image} .
For vectors {image} , find u + v. Select the correct answer:
CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.
Presentation transcript:

Find the cross product {image} . {image} . 1. {image} 2. 3. 4. 5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find {image} correct to three decimal places where {image} . 3.441 35.973 44.234 30.973 5.162 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Use the scalar triple product to identify the coplanar vector(s) below Use the scalar triple product to identify the coplanar vector(s) below. Select the correct answer(s). 1. {image} None of these 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A wrench 20 cm long lies along the positive y - axis and grips a bolt at the origin. A force is applied in the direction {image} at the end of the wrench. Find the magnitude of the force needed to supply 60 J of torque to the bolt. F=228N F=843N F=158N F 949N F =316N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Let P be a point not on the plane that passes through the points Q, R, and S. Use the formula for the distance d to the plane {image} where {image} to find the distance from the point P ( -1, 4, 3 ) to the plane through the points Q ( -1, -2, 3 ), R ( 3, -3, 1 ) and S ( -3, -1, 2 ). d = 8.9 d = 5.5 d = 13.7 d = 5.6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50