Vector Addition 101

Today in class we began talking about Vector Addition. Any vectors may be added algebraically if they are collinear. The vector sum of 2 or more vectors is called the resultant vector. For example, 5cm [W], 7cm [W] and 3cm [E] can all be added together.

A negative vector means that it`s direction is exactly opposite of the direction it is stated. For example, -3cm [N] = 3cm [S].


Example 1: Determine algebraically the result vector of the picture below.
5km [N 43° W] + 4km [N 43° W] = 9km [N 43° W]

Adding Vectors Graphically
We add vectors graphically when the vectors are non-collinear; since they cannot be added algebraically.

Steps to adding vectors graphically:
1. Decide on a scale and draw your reference coordinate to the right of your page.

2. Indicate the starting point of your first vector with an X

3. Draw one of the vectors placing its tail at the X.
**Remember to label all vectors with a magnitude and a direction!**

4. Draw your next vector starting at the tip (the arrow head) of the previous vector you drew. Do this step until all the vectors in the question have been drawn.

5. Draw a dotted line from the X to the terminal point of your final vector. This new vector represents the vector sum (resultant vector).

6. Measure the resultant vector and determine its direction from the starting point X using a protractor.

Example 2: Sally walks 3km [S], 5km [E], 2km [S] and 4km [W]. Determine the resultant vector.

Jordan Grywacheski is up next.