Physics
Abbott
Name: ___________________ Date: _________
Period: _____
What’s our vector, Victor?
Vectors are amazing things. They provide us with a mathematical way to show
magnitude and direction. They are numbers that point somewhere. Like numbers,
we can do mathematical operations (addition, subtraction, multiplication) with
vectors. However, as you might imagine, this gets a little more complicated (not a
lot, just a little).
This worksheet/activity should help you figure out how to add and subtract vectors.
There are some very neat tricks when it comes to working with vectors. Hopefully
you will see this after a bit of work.
Adding Vectors
You will need the following materials:
 Graph paper
 At least three fingers: a thumb, pointer finger, and pinky. If this is a
problem, notify Mr. Abbott and he will let you borrow his own.
1. Create an origin for your graph at the bottom left of the paper.
2. Place your fingers on the graph paper (in your best emperor-making-alightning-bolt-with-the-force fashion). Make sure the tip of your thumb is
placed on the origin.
3. Using a pen or pencil, mark the position of each of your fingertips.
4. Draw vectors to each finger tip. Using the units on the graph paper, write the
vectors using vector notation <x,y> for each finger (call them rpinky, rpointer,
rmiddle, and so on).
Vectors:
Physics
Abbott
Name: ___________________ Date: _________
Period: _____
5. We are going to add two vectors: your pinky vector, and your pointer finger
vector. To do this, we simply add the components to form a new vector.
Mathematically, we would write:
𝑟⃑𝑝𝑖𝑛𝑘𝑦 + 𝑟⃑𝑝𝑜𝑖𝑛𝑡𝑒𝑟 =< 𝑥𝑝𝑖𝑛𝑘𝑦 + 𝑥𝑝𝑜𝑖𝑛𝑡𝑒𝑟 , 𝑦𝑝𝑖𝑛𝑘𝑦 + 𝑦𝑝𝑜𝑖𝑛𝑡𝑒𝑟 >
Write the new vector in vector notation. Call it r1.
⃑⃑𝟏 =
𝒓
6. Draw the new vector (the vector sum). Label it.
7. Get a new piece of graph paper (I know, how wasteful. You will be using
lots of graph paper). We’re going to try something different.
8. Pick either your pinky vector or your pointer vector and draw it from the
origin using the same components from the previous graph.
9. After you have drawn this vector, draw the other one. However, start
drawing it (using the same components from the last graph) from the tip of
your previous vector.
10.After you have drawn both vectors in this manner, start a new vector from
the start of your first vector to the tip of your second vector. Find the
components of this new vector and write them below in vector notation. Call
it r2.
⃑⃑𝟐 =
𝒓
11.Compare the new vector from step 10 to the vector you got in step 6. How
do they compare?
12.Can you make any conclusions about how to add vectors on a graph?
13.Use your answer from number 12 to make a prediction about how you might
add more than two vectors on a graph.
Physics
Abbott
Name: ___________________ Date: _________
Period: _____
14.Now go back to the first graph you made. Things are going to get crazy: I
want you to add all four of your finger vectors. To do this, add each
component. You may need to ask Mr. Abbott for help on this one. Write the
sum of all these vectors below as a new vector, r3.
⃑⃑𝟑 =
𝒓
15.Draw r3 on your second graph.
16. Now on your second graph, draw the rest of your finger vectors in the same
way you did for steps 8 and 9. Always start a new vector at the tip of the last
one.
17.What do you notice?
Subtracting Vectors
1. Get a fresh new piece of graph paper. I know, this is number three.
2. Redraw your finger vectors on this graph paper. Use the same components
from your first piece.
3. You are going to subtract your pointer vector from your pinky vector. To do
this, subtract the pointer components from the pinky components.
Mathematically,
𝑟⃑𝑝𝑖𝑛𝑘𝑦 − 𝑟⃑𝑝𝑜𝑖𝑛𝑡𝑒𝑟 =< 𝑥𝑝𝑖𝑛𝑘𝑦 − 𝑥𝑝𝑜𝑖𝑛𝑡𝑒𝑟 , 𝑦𝑝𝑖𝑛𝑘𝑦 − 𝑦𝑝𝑜𝑖𝑛𝑡𝑒𝑟 >
Write this new vector below in vector notation. Call it r4.
⃑⃑𝟒 =
𝒓
4. Now draw this vector on your graph, but with these rules: start at the tip of
the pinky vector.
Physics
Abbott
Name: ___________________ Date: _________
Period: _____
5. Where does the vector end?
6. Can you make a prediction of what would happen if you subtracted multiple
vectors?
7. Now subtract all of the other finger vectors from your pinky vector. To do
this, subtract the components (xpinky – xring – xmiddle – xpointer ). Write this new
vector in vector notation below, and call it r5.
⃑⃑𝟓 =
𝒓
8. Again, draw this new vector, but start at the tip of your pinky vector. Where
does it end?
Conclusion
Sum up your findings during this activity in the following questions:
1. How do you add vectors on a graph?
2. How do you subtract vectors on a graph?