http://www.ck12.org Chapter 7. Vectors
7.1 Basic Properties of Vectors
Here you will find out what a vector is algebraically and graphically.
An airplane being pushed off course by wind and a swimmer’s movement across a moving river are both examples
of vectors in action. Points in the coordinate plane describe location. Vectors, on the other hand, have no location
and indicate only direction and magnitude. Vectors can describe the strength of forces like gravity or speed and
direction of a ship at sea. Vectors are extremely useful in modeling complex situations in the real world.
What are other differences between vectors and points?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61366http://www.youtube.com/watch?v=IKzR0Odurm0 James Sousa: Introduction to Vectors
Guidance
A two dimensional vector is represented graphically as an arrow with a tail and a head. The head is the arrow and is
also called the terminal point. When finding the vector between two points start with the terminal point and subtract
the initial point (the tail).
The two defining characteristics of a vector are its magnitude and its direction. The magnitude is shown graphically
by the length of the arrow and the direction is indicated by the angle that the arrow is pointing. Notice how the
following vector is shown multiple times on the same coordinate plane. This emphasizes that the location on the
coordinate plane does not matter and is not unique. Each representation of the vector has identical direction and
magnitude.