2. Geometric Vector Arithmetic
- Author:
- Justin Mears
Instructions:
In this activity we are going to investigate geometric vector arithmetic.
Complete all of the following activities in the first graphics window below.
Now, let's begin by plotting a couple vectors.
Part 1:
In the graphics box below, plot the vector a = , by typing "a = vector((2,2))" into Geogebra, and the vector b = similarly.
Next, type the following into the third input box of Geogebra:
c = a + b
which gives us the vector c resulting from the sum of the vectors a and b.
"What a minute!" you exclaim, "I thought Justin Ryan told us that the resultant vector of a sum would be given by putting the tail of one vector to the tip of the other! Isn't a parallelogram involved?!"
Yes! You are correct! So, let's make that happen.
Part 2:
In your input window, you should see that the resultant vector c = (does this make sense from what you know about algebraic vector addition?).
Noting that the terminal point of c is , plot the vector u with initial point and terminal point and the vector v with initial point and terminal point .
This returns the (expected) parallelogram and we gain a little more insight about vector equivalence, that is, we see that a = v and b = u.
Part 3
In the next graphics window, play around with vector subtraction in a similar way to what we did for vector addition. Using the same vectors from Part 1 investigate the following ideas.
What happens when you enter "a - b" into the input bar? Does it compare with your expectations from lecture?
Can you do some similar manipulations to geometrically show why the resulting vector from that subtraction does or does not make sense?