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.
2. • 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
3. 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
4. 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