In this lesson, you will learn about vectors by their basic definitions, distinguish vectors from scalars, get to know the basic operations on vectors geometrically and algebraically, learn about the properties of vector operations, and applications of vectors in 2D.
View all of the instructional videos, read the provided reading, and practice exercise/activities. These will help you master the objectives for this lesson. Pay attention to additional comments provided. A good understanding of how vectors operate in 2D will help you master the concepts in Lesson 1.3, when the vectors are extended to 3D. It is important that you use proper notation for vectors in your written work. Also, it is important that you know how to construct vector addition, subtraction, scalar multiplication and vector components both geometrically and algebraically.
Upon completion of lesson 1.1, you will be able to:
Identify and construct vectors
Perform vector addition, subtraction, and scalar multiplication both geometrically and algebraically
Determine magnitudes and unit vectors
Recognize and apply properties of vector operations
Model and solve applications
View all of the following instructional videos. These will help you master the objectives for this lesson.
Introduction to Vectors and Scalars [8:39]
Source: KhanAcademy from YouTube
Vector Basics [11:32]
Drawing Vectors/Vector Addition Part 1
Source: patrickJMT from YouTube
Note: The sound of the videos from "patrickJMT" is poor, so start with low volume (especially if you are using headphones) and then adjust accordingly.The presenter called the tail of a vector “tip” and tip/head of a vector “tail.” Continue to Part 2 below.
Vector Basics - Part 2 [5:35]
Algebraic Representations
Source: patrickJMT from YouTube
Equivalent Vectors [1:55]
Source: SOPHIA
Note: After watching the video, don't forget to take the quiz on the right.
Zero Vectors [3:14]
Source: SkyingBlogger from YouTube
Vector Operations [9:05]
Source: bullcleo1 from YouTube
Note: Please watch through to the 5:00 minute mark. This video also covers other concepts for future lessons.
Finding a Unit Vector - Ex.1 [2:07]
Source: patrickJMT from YouTube
Finding a Unit Vector - Ex.2 [4:55]
Source: patrickJMT from YouTube
Note: Ex 2c, you should be able to find the unit vector without any computation.
Vector Applications [9:03]
Source: bullcleo1 from YouTube
Warning: The presentation of the solutions to the two problems is sloppy. When you do your “Show Your Work Assignment” you need to present your work formally, not like the presenter. What he does on the video is more like what you do on a scratch paper.
Applications of Vector Addition.avi [8:40]
Source: AlRichards314 from YouTube
Warning: You may want to round the final answer to avoid rounding error. For example, you may round to the nearest integer for the magnitude of the vector. However, when you try to find the angle, you may not want to substitute the rounded integer value for the magnitude of the vector.
Adding Vectors: How to Find the Resultant of Three or More Vectors [14:43]
Source: PhunScience from YouTube
Note: This video has good visual representation. However, the presenter forgot to use the degree sign. Recall that in writing, cos 45 means cosine of 45 radians and cos 45∘ means cosine of 45 degrees. You must make the distinction when presenting your work.
The following required readings cover the content for this lesson. As you go through each reading, pay close attention to the content that will help you learn the objectives for this lesson.
3.2 Vector Addition and Subtraction
There is a typo: when it talks about the Law of Sines, the angle “q” between C and A, it should be the angle . between C and A.
Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.
[Leading Lesson](27 problems with solutions), vector addition (10 problems with solutions), vector subtraction (17 problems with solutions), vector scalar multiplication (5 problems with solutions) It covers more than what is in lesson 1.1. dir x⃗ means the unit vector in the direction of vector x⃗ .
Cut The Knot
The above game is a Flash-based game that is an interactive way to understand direction of motion and vectors.
Cite: A. Bogomolny, Vector Addition and Subtraction from Interactive Mathematics Miscellany and Puzzles http://www.cut-the-knot.org/Games/Vectors.shtml, Accessed 15 February 2013
Below are additional resources that help reinforce the content for this lesson.
Unit Vectors (video) [8:50]
Source: bullcleo1
Note: This video contains a common mistake. When referring to the leg of the reference triangle, the presenter assigned a negative value (-1/2) as the length of the leg. Instead, the presenter should have said the tip of the vector has x-coordinate -1/2. Be aware of this common mistake, I will not point it out every time it occurs on a video.
Unit Vectors and Engineering Notation (video) [7:58]
Khan Academy
Note: The writing is sloppy in this video but the information is still relevant.
Do Homework 1.1 on MyMathLab.
Show Your Work assignment will be given via Assignment Tool on Laulima. Please check your email for Laulima announcement.