Section: Module 7: Lesson 1: Vectors and Scalars | Intro to Algebra & Trigonometry | NextGenU.org

  • Student Learning Outcomes:
    Upon completion of this lesson, you will be able to:
    • Distinguish between vector and scalar quantities.
    • Identify the standard form or position vector.
    • Identify the different types of vectors.
    • Identify displacement vectors.
    • Determine vector equality graphically.
    • -Given an initial and a terminal point, find the position vector represented.
    • Find the magnitude of a two-dimensional vector.
    • Find the direction of a two-dimensional vector.
    • Use the position vectors to determine vector equality.

    Approximate time required for the readings for this lesson (at 144 words/minute): 5 hours and 41 minutes.

    Click here to start this lesson
    • Required Learning Resources and Activities
    • Read the entire page. (6 minutes)

      NASA GRC - 2021

    • Read Sections 10.1: Introduction Page 424, Section 10.2: Some Basic Concepts Page 425 (Omit Direction Cosines), and Section 10.3: Types of Vectors - Pages 427-428, and do the 5 questions of Exercise 10.1 for internalization of the concepts. (20 min)

       NCERT - 2020

    • Read Section 10.8.1: Vewing Vectors Geometrically - pages 1178-1180. (10 minutes)

      OpenStax, Rice University - 2015

    • Read Section 10.8.1: Vewing Vectors Geometrically - pages 1178-1180. (7 minutes)

      OpenStax, Rice University - 2015

    • Read Section 10.8.2: Find the Magnitude and Direction of a Vector - Pages 1181-1183. (10 minutes)

      OpenStax, Rice University - 2015

    • In this activity, you will visit some sites and use some of the applet animations found there to explore vectors close up.

      Step 1. Explore

      Explore some of the applet animations found here to explore vectors close up. Move the vectors around by grabbing their endpoint dots; change their lengths and locations and see how they behave. This will help you to gain a better understanding of vectors.

      1. Collinearity

      This applet demonstrates the concept of vector collinearity. Follow this link.
      Demonstration colinearity – GeoGebra

      1. Vectors in Standard Position

      This applet will help you to understand by seeing what is meant by a vector being in the standard position.
      Angles in Standard Position – GeoGebra

      1. The four applets in this section demonstrate vector addition.

      Definition of vector addition – GeoGebra
      Move the red dots to change the lengths of the vectors u and v. Observe the resultant vector u+v.

      Addition of vectors – GeoGebra
      Two separate vectors with shown coordinates are added together. The resultant vector appears in blue and its coordinates are shown. Understand how they arrived at the coordinates of the vector sum.

      Vector Addition – GeoGebra
      Sum of several vectors placed end-to-end. Move the points to change their lengths and locations

      Resultant of Two Forces – GeoGebra
      Resultant of Two Forces

      4. This is the applet that demonstrates the graphing of points at different coordinates in Octant 1 of the 3-D system.

      5. This applet demonstrates the entire 3-D system with its 8 octants. You can pull the corners around  to view the octants from different angles.

      Step 2. Study

      Study and manipulate this applet more deeply. You will answer a case problem after exploring this app.

      Step 3. Analyze

      Analyze and answer the questions at the end of the applet exercise from Step 2.

      Step 4. Respond

      Respond by writing a 200-500 word review of all the applet animations explored. Please include the following:

      • Purpose of the applet animations
      • Distinct features
      • Pro’s and con’s of using the applet to learn vectors

      As for the Relative velocity: Boat problem – GeoGebra animation, respond by showing all the steps you take to solve this problem, and the theorems, properties, or laws you used to enable you to move from step to step in the solution.

      Step 5. Share

      To share your work, click on the “Add a new discussion topic” button under this post and paste your work in the “Message” box. Make sure to reference others’ intellectual property when necessary. All references should follow 7th Edition APA formatting. For further instructions, see the resource on the Himmelfarb Health Sciences Library: APA citation resource (N.B. references are excluded from word counts).

      Step 6: Interact

      To complete the activity, you will need to reply to at least two posts made by your peers in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “post to the forum.”

      OPTIONAL Step 7: Interact (10 minutes)

      If you would like to, you can reply to your peers' posts in a respectful and professional manner. Ensure that your post engages your peers' ideas by including a reflection on their comments, sharing ideas of other potential difficulties and parties involved, or asking thought-provoking questions. If a peer comments on your posting, please reply. To post a reply, click “Reply” on a particular discussion, write your feedback and then click on “Post to forum.”


    • quiz icon
      Quiz: Module 7: Lesson 1

      To access the quiz, click on the name of the quiz provided above. On the following screen, click the "Preview quiz now" button to respond to the questions.

      TO PASS THIS QUIZ YOU MUST OBTAIN A SCORE OF 7/9

      Not available unless: The activity Quiz: Module 6: Lessons 3 - 4 is marked complete