Writing Assignment 4, Last writing assignment worth 20 points

This is a combination of a writing assignment and some experiments. Do all of the steps in the experiments and answer the questions. This assignment is a bit longer than your other writing assignments so it is worth twice the points and this will be your last writing assignment. Please complete the experiments and draw your conclusions before your next test. By test 4 review day, I want to see that you have done the experiments and written a rough draft of your conclusions. You may turn in a nicer writing on the day after the test. If you get a chance to turn in either a rough draft or a final write up before the review day, I can give you feedback before the test. This can be helpful to make sure you have the concepts correct before the next test. There will be time to work on this experiment in class. You might be able to get the rough draft done in class. I recommend getting two printouts each time a print is called for, so you can use one to write on for your rough draft and you can use the other for your final write up.

These equations will be referenced throughout this assignment.

  1. Let u = ai + bj
  2. Let v = ci + dj
  3. Let p = ru + sv

Pick 6 different non-zero integer values for a, b, c, d, r, and s. Use values between -8 and 8 for letters a, b, c, and d and values between -3 and 3 for r and s. If you choose a value of one for r or s, do not choose negative one for the other. Write down the values you have chosen in the space above. Do not pick values the same as others near you.

Experiment 1

Step 1: Use the Vector Drawing Board to make vectors u and v.

Step 2: Duplicate u, |r| times. (Negate before you duplicate if r is negative.)

Step 3: Duplicate v, |s| times. (Negate before you duplicate if s is negative.)

Step 4: Drag the vectors to put them into position to add.

Step 5: Add the vectors to make vector p.

Step 6: Print the results.

Step 7: Answer the following questions and elaborate where needed:

What are the components of p? If you were given a similar problem now, how could you figure p's components without doing an experiment? Compare |p| with |u| and |v|. What happens if you replace the vectors with their magnitudes in equation 3?

 

Experiment 2

Start with where you left off in experiment 1. In other words do not reset the drawing board.

Step 1: Break all of your vector u's and vector v's into their component parts and then delete the original vectors or move them out of the way.

Step 2: Drag the component parts into position to add them.

Step 3: Do whatever is needed to compare the sum of the component parts with the sum of the vectors. (You decide how to handle this step.)

Step 4: Print your results.

Step 5: What conclusions do you arrive at from this experiment?

Step 6: Also take a look at the component parts of your resultant vector.

Step 7: Print again.

Step 8: Compare the components of the resultant to the components of the vectors you are adding. What do you discover?

 

Other Questions to Answer,

Devise experiments to answer these if needed. You do not have to print these, but you can if it helps you explain your answer.

question 1: Does the order of addition of vectors matter?

question 2: Is the angle of the resultant vector equal to the sum of the angles of the vectors that you are adding? I.e. Can you apply equation 3 to the angles?

question 3: Thinking back to experiment 1, under what conditions is the magnitude of the resultant vector equal to the magnitude of the vectors you are adding. I.e. When can you apply equation 3 to the magnitudes?

Bonus Problem

(5 extra points if you do this by end of class and illustrate it on the Drawing Board, 3 extra points if you can do it by the beginning of the next class and bring in your drawing board printout to illustrate it. Make sure you write your equation on the printout.)

Let m = 2i - j.
Let n = i + 3j.
Let q = -6i + 17j.

Draw m,n, and q on the drawing board and then show that q is a linear combination of m and n. After you show this on the drawing board, write the equation that shows q as a linear combination of m and n.