ENGI 1313 Mechanics I

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# ENGI 1313 Mechanics I - PowerPoint PPT Presentation

ENGI 1313 Mechanics I . Lecture 07: Vector Dot Product. Chapter 2 Objectives. to review concepts from linear algebra to sum forces, determine force resultants and resolve force components for 2D vectors using Parallelogram Law to express force and position in Cartesian vector form

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### ENGI 1313 Mechanics I

Lecture 07: Vector Dot Product

Chapter 2 Objectives
• to review concepts from linear algebra
• to sum forces, determine force resultants and resolve force components for 2D vectors using Parallelogram Law
• to express force and position in Cartesian vector form
• to examine the concept of dot product
Lecture 07 Objectives
• to examine the concept of dot product
Overview of Dot Product
• Definition
• Laws of Operations
• Commutative law
• Scalar Multiplication
• Distributive law
Overview of Dot Product (cont.)
• Dot Product of Cartesian Vectors

Go to zero

Application of Dot Product
• Angle between two vectors
• Cables forces and the pole?
• and ?

Component magnitudes

If A||has + sense then same direction as u

^

Application of Dot Product (cont.)
• Component magnitudeof A on a parallel or collinear linewith line aa
• Recall

Component A||

Application of Dot Product (cont.)
• The vector A|| canbe determined by:

Vector A||

Application of Dot Product for Component A||

Multiply by Unit Vector ûto obtain Vector A||

Application of Dot Product (cont.)
• For force vector F at Point A: What is the component magnitudeparallel (|F1|) to the pipe (OA)?
Application of Dot Product (cont.)
• For force vector F at Point A: what is the component magnitudeperpendicular (F2) to the pipe (OA)?
• Method 1
• Method 2
Comprehension Quiz 7-01
• The dot product of two vectors results in a _________ quantity.
• A) scalar
• B) vector
• C) complex number
• D) unit vector
AExample Problem 7-01
• For the Cartesian force vector, find the angle between the force vector and the pole, and the magnitude of the projection of the force along the pole OA
AExample Problem 7-01 (cont.)
• Position vector rOA
• Magnitude of |rOA|
• Magnitude of |F|
AExample Problem 7-01 (cont.)
• Find the angle between rOA and F

AExample Problem 7-01 (cont.)
• Find magnitude of the projection of the force F along the pole OA

Comprehension Quiz 7-02
• If the dot product of two non-zero vectors is 0, then the two vectors must be ______ to each other.
• A) parallel (pointing in the same direction)
• B) parallel (pointing in the opposite direction)
• C) perpendicular
• D) cannot be determined.
Comprehension Quiz 7-03
• The Dot product can be used to find all of the following except ____
• A) sum of two vectors
• B) angle between two vectors
• C) vector component parallel to a line
• D) vector component perpendicular to a line