3.2: Adding and Subtracting Vectors
When adding or subtracting vectors, we can follow many of the rules we learned in math class about non-vector numbers. Vector addition follows the commutative property, which means the order of addition does not matter. Vector addition also follows the
associative property, which means it does not matter which vector is first when vectors are being added.
One way to add or subtract vectors is to do so graphically. The graphical method for adding and subtracting vectors is called the head-to-tail
method. When adding vectors using this method, use these steps:
1. Draw the first vector starting from the tail, or starting point of the vector, to its head, or ending point (arrow) of the vector.
2. Begin the second vector by putting its
tail at the head of the first vector.
3. Finally, draw a line from the tail of the first vector to the head of the second vector.
The vector that results is the resultant vector, or the solution to the vector addition problem. To determine
the magnitude of the resultant vector, measure it with a ruler. To determine the direction of the resultant vector, use a protractor to determine the angle from one of the axes. When subtracting vectors graphically, consider the vector that is being
subtracted as negative. That means the direction of the vector being subtracted is flipped so it points in the opposite direction. The head-to-tail process is the same as it is for addition.
As you read, pay attention to the worked examples: using the head-to-tail method to add multiple vectors in Example 3.1 and using the head-to-tail method to subtract vectors in Example 3.2.