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Vector Lesson


Shodor > CSERD > Resources > Activities > Vector Lesson

  Lesson  •  Materials  •  Lesson Plan


Lesson Plan - Vectors

Suggestions for Instructors

The Vector Calculator is designed to help students understand the connection between a vector's magnitude and direction and its representation in x-y coordinates.

One of the most common problems students have when facing problems in introductory physics courses is a poor understanding of vectors. Students often forget to convert a vector into x and y coordinates before solving a problem.

Standards

NCTM Grades 6-8 Geometry:
  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems
    • Use coordinate geometry to represent and examine the properties of geometric shapes;
  • Use visualization, spatial reasoning, and geometric modeling to solve problems
    • Draw geometric objects with specified properties, such as side lengths or angle measures;
    • Use visual tools such as networks to represent and solve problems;
    • Use geometric models to represent and explain numerical and algebraic relationships;
    • Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.

Solutions

* All angles in degrees.

  1. position, vector; length, scalar; force, vector; temperature, scalar; torque, vector; price, scalar.
    • q = 45, x positive, y positive
    • q = 120, x negative, y positive
    • q = 120, x negative, y zero
    • q = 200, x negative, y negative
    • q = 300, x positive, y negative
  2. Values are approximate:
    • r = 3, q = 180, x = -3, y = 0
    • r = 2, q = 195, x = -1.9, y = -0.5
    • r = 5, q = 45, x = 2.2, y = 2.2
    • r = 1, q = 120, x = -0.5, y = 0.86
    • r = 1, q = 323, x = 0.80, y = -0.60
  3. Values are approximate:
    • x = 2, y = 2, r = 2.8, q = 45
    • x = 1, y = -1, r = 1.4, q = 315
    • x = 3, y = -2, r = 3.6, q = 326
    • x = 0, y = -3, r = 3, q = 270
    • x = -2, y = 1, r = 2.2, q = 153

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