Worksheet on working with vectors, including definitions, examples, and graphing exercises for understanding vector addition and subtraction.

Let’s solve this step by step.

We are given a vector problem on a grid. The task is to find the resultant vector when adding two vectors: a and b.

From the diagram (left side, “Example 1”):

- Vector a goes from point A to point B.
- Vector b goes from point B to point C.
- We are told that vector a = AB, and vector b = BC.
- We need to find what a + b equals — which should be the vector from start to end: A to C.

Looking at the coordinates or movement:

Assume each square is 1 unit.

Vector a (AB):
- From A to B: moves right 3 units, up 2 units → so a = (3, 2)

Vector b (BC):
- From B to C: moves right 1 unit, down 4 units → so b = (1, -4)

Now add them:

a + b = (3 + 1, 2 + (-4)) = (4, -2)

That means the resultant vector moves 4 units right and 2 units down.

Now look at the options given in Example 1:

a. a + b

b. A + C ← This doesn’t make sense — you can’t add points like that.

c. AC ← This is the vector from A to C — which is exactly what we got!

d. B + A ← Again, adding points isn’t valid for vectors.

So the correct answer is c. AC

But wait — let’s double-check with the graph.

If you go from A to B (vector a), then from B to C (vector b), your total displacement is from A to C — which is vector AC.

Yes — that matches our calculation: (4, -2)

Also, note that in vector addition, a + b = AC because it’s the head-to-tail method.

Final Answer:
c. AC