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

• 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