text: # ENGI 1313 Mechanics I - PowerPoint PPT Presentation
  
  1 / 20
  
  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
  
  I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
  
  ENGI 1313 Mechanics I
  
  Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
  
  - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
  
  ## 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
  
  A
  
  ### Example 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
  
  A
  
  ### Example Problem 7-01 (cont.)
  
  • Position vector rOA
  
  • Magnitude of |rOA|
  
  • Magnitude of |F|
  
  A
  
  ### Example Problem 7-01 (cont.)
  
  • Find the angle between rOA and F
  
  A
  
  ### Example 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
  
  ### Comprehension Quiz 7-04
  
  • Find the dot product (PQ) for
  
  • A) -12 m
  
  • B) 12 m
  
  • C) 12 m2
  
  • D) -12 m2
  
  • E) 10 m2
metadata: {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}