Unit vectors

The  exercise appears under the Precalculus Math Mission. This exercise discovers various properties about the unit vector, a vector of length one.

Types of Problems
There are four types of problems in this exercise:


 * 1) Find a lengthened vector: This problem provides a unit vector by it's component form. The student is expected to find the components of an elongation of the vector.Uv1.png
 * 2) Write the vector as multiple of unit vector: This problem provides a vector that is not necessarily of unit length. The student is expected to take the vector and write it as a multiple of a unit vector.Uv2.png
 * 3) Write in component form and provide length: This problem describes a vector. The student is expected to write the vector using the component form and also provide it's correct length in the space provided.Uv3.png
 * 4) Determine which are unit vectors: This problem has a graphic with several vectors pictured on it. The student is expected to select all of these vectors which happen to have unit length.Uv4.png

Strategies
Knowledge of how to calculate and picture the magnitude (length) of a vector are encouraged to ensure success on this exercise.
 * 1) The length of a vector is sqrt(x^2+y^2) where the vector is written in the form .
 * 2) To make a vector unit length, divide the vector by it's magnitude.

Real-life Applications

 * 1) Vectors are used to represent quantities that have size and direction.
 * 2) Forces, such as gravity, are vector quantities and are found often in physics.
 * 3) The magnitude and direction of a vector can be used to represent motion that would not be considering a proper function.