Certain quantities, like the temperature or the score of a game, measure only the magnitude of something.
Other quantities are more than just the magnitude of something. They also have a directional component to them.
Quantities with magnitude and direction are called vectors
Vectors with the same magnitude and direction are considered identical. All of these arrows represent the same vector.
A vector is a mathematical object for which a natural operation of addition exists.
Two methods used to find vector sums, called resultants, are called the Parallelogram method and the Tip-to-tail method.
With the parallelogram method, the two vectors to be added are thought of as the non-parallel sides of a parallelogram with a common tail.
The resultant vector is the vector that coincides with a diagonal of the parallelogram and also has the same common tail as the two addend vectors. The arrowhead of the resultant is at the other endpoint of the diagonal.
With the tip-to-tail method, the vector representing the second addend is placed so that its tail coincides with the tip of the vector representing the first addend.
The resultant vector is the vector that shares its tail with the first addend and its tip with the second addend.
The purpose of this simulation is to allow you to experiment with the two vector addition methods.
You will need to enter two vectors and then decide on the method used to add them. You can also choose how to display coordinate systems, if any.
The vectors may be entered by using the sliders beneath the entry fields, or by typing their x and y components or the direction and distance in the entry fields. The vector’s tail will be located at the origin.
A vector may also be entered by clicking in an entry field for the vector and then clicking the location of its tip in the drawing area.
After two vectors are entered, select an addition method. The resultant will be plotted in the drawing area and its numeric information will be displayed in the control area.
The vectors may be adjusted after they are added by entering new values or by dragging the tips of the arrows to different locations.
To drag vector B after the tip-to-tail addition method, use the drag point, appearing at the original location of the tip of the vector.
Answer the Practice Questions and think about the Explorations and you’re off to an understanding of vector addition.