Adding vectors in magnitude and direction form

The  exercise appears under the Precalculus Math Mission. This exercise plays with the magnitude and direction form of a vector.

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


 * 1) Find the requested component: This problem provides some vectors in magnitude/direction form. The student is asked to find the value of a particular component after the vectors have been combined.Avimadf1.png
 * 2) Compare the sizes: This problem provides vectors that are being added or subtracted. The student is asked to use the given information and determine the correct inequality to place on the vector expressions.Avimadf2.png
 * 3) Find the magnitude and direction: This problem provides some information about some vectors. The student is expected to use this information and provide the correct magnitude and direction for the vector.Avimadf3.png

Strategies
Knowledge of the transfer between rectangular and polar coordinates are encouraged to ensure success on this exercise.
 * 1) The horizontal component of a vector with magnitude r and angle theta is rcos(theta).
 * 2) The vertical component of a vector with magnitude r and angle theta is given be rsin(theta).

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.