Graphically adding and subtracting vectors

The  exercise appears under the Precalculus Math Mission. This exercise experiments with adding vectors in a primarily graphical setting.

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


 * 1) Write an equation for the picture: This problem has a drawing of a triangle made of vectors. The student is asked to give a correct vector equation that models the relationship in the drawing.Gaasv1.png
 * 2) Graph the terminal point: This problem has a coordinate plane with two vectors. The student is asked to give the terminal point of a vector that results from either adding or subtracting the vector quantities.Gaasv2.png
 * 3) Determine which pictures are accurate: This problem has an initial coordinate plane with two vectors drawn. Following this, there are two more pictures that may or may not contain correct interpretations of addition and subtraction of these vectors. The student is asked to select whether one, both or neither of the pictures have a correctly drawn relationship.Gaasv3.png

Strategies
Knowledge of arithmetic operations on vectors is encouraged to ensure success on this exercise.
 * 1) Vectors are added "head-to-tail" which means one should be drawn and the other drawn from the first one's ending head.
 * 2) Subtraction for vectors is adding the opposite, where the opposite means the vector has the same components but is going in an opposite direction.
 * 3) In the Write an equation for the picture problem, if the vectors all flow in one direction pretend one is the opposite (the negative one, if possible) and then it is possible to see the point where two paths end. This can make it more direct to find the arithmetical relationship between the vectors.

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) Vectors can be used to model motion of airplanes and ships that are affected by winds and tides.