Vectors in 2D
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).
- 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.
- 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