The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors that make a right angle to each other. the head-to-tail method using a scaled vector diagram.the Pythagorean theorem and trigonometric methods.The two methods that will be discussed in this lesson and used throughout the entire unit are: There are a variety of methods for determining the magnitude and direction of the result of adding two or more vectors. The vector sum will be determined for the more complicated cases shown in the diagrams below. For example, a vector directed up and to the right will be added to a vector directed up and to the left. In this unit, the task of summing vectors will be extended to more complicated cases in which the vectors are directed in directions other than purely vertical and horizontal directions. Sample applications are shown in the diagram below. These rules for summing vectors were applied to free-body diagrams in order to determine the net force (i.e., the vector sum of all the individual forces). Observe the following summations of two force vectors: During that unit, the rules for summing vectors (such as force vectors) were kept relatively simple. That is the net force was the result (or resultant) of adding up all the force vectors. Recall in our discussion of Newton's laws of motion, that the net force experienced by an object was determined by computing the vector sum of all the individual forces acting upon that object. This process of adding two or more vectors has already been discussed in an earlier unit. Two vectors can be added together to determine the result (or resultant). One such operation is the addition of vectors.
A variety of mathematical operations can be performed with and upon vectors.
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