Components of vectors

The  exercise appears under the Precalculus Math Mission. This exercise concentrates on the rectangular components (horizontal and vertical) that make a vector.

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


 * 1) Write the components in the picture: This problem has a vector drawn on the coordinate plane. The student is asked to look at the graph and find the horizontal and vertical components of the vector.Cov1.png
 * 2) Find the components in context: This problem describes how a vector moves from one place to another or where it starts and ends. The student is expected to carefully read the question and use knowledge of vectors to find the components of a vector from the description.Cov2.png
 * 3) Answer question based on picture: This problem provides a large coordinate plane with several vectors drawn on it. The student is asked to use the picture to find all vectors that satisfy some condition described in the problem.Cov3.png

Strategies
Knowledge of arithmetic operations on vectors and the rectangular form of a vector are encouraged to ensure success on this exercise.
 * 1) The horizontal component is often referred to as an "x-coordinate" and the vertical is like a "y-coordinate."
 * 2) The questions in the Find the components in context problem ask for where a vector ends, or where it begins. It is necessary to read carefully on this problem.
 * 3) Examples of questions in the Answer question based on picture problem are finding all vectors with the same horizontal motion, or vertical motion.
 * 4) If a vector goes from (x1,y1) to (x2,y2) then it's components are (x2-x1,y2-y1). However, it is sometimes more straightforward to just think how one can move from the beginning to the end.

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.