Subject:
Higher Education, Mathematics, Calculus, Geometry, Physics
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Algebra of Vectors, Component Form, Direction, Magnitude, Mathematics, Tmm0022, Trigonometric Form, Unit Vector
License:
Creative Commons Attribution-NonCommercial 4.0
Language:
English
Media Formats:
Text/HTML

Vectors in 2D

Module Overview

Vectors - magnitude, direction, component form, trigonometric form, unit vector, algebra of vectors, applications,

TMM 002 PRECALCULUS (Revised March 21, 2017)

AdditionalOptional Learning Outcomes:

2. Geometry: The successful Precalculus student can:

2e. Interpret the result of vector computations geometrically and within the confines of a particular applied context (e.g., forces).
Sample Tasks:

  • The student can define vectors, their arithmetic, their representation, and interpretations.
  • The student can decompose vectors into normal and parallel components.
  • The student can interpret the result of a vector computation as a change in location in the plane or as the net force acting on an object.

Section 1: Vectors

We will learn about two-dimensional vectors which are quantities that have both magnitude and direction.

Learning Objectives:

  • Definition of a vector and its component form
  • Equality of two vectors
  • Vector arithmetic and properties
    • Vector Addition
    • Scalar Multiplication
  • Magnitude and direction of a vector, and their properties
  • Unit vector
  • Principal unit vector in the direction of positive x and y axes
  • Writing a vector in different forms
    • component form
    • principal unit vector form
    • magnitude and cosine and sine functions
  • Application to equilibrium of forces acting on a body