1. Adding Vectors Graphically
Why it is a good idea to pay attention when Mr. Calderón gives examples

2. Recall… Scalars have magnitude, or a measured amount, such as 25.5 kg.
Vectors have both magnitude and direction, such as m/s, East.
For scalars, = 7 is always true.
For vectors, = 7, or it can equal 1, or it can equal 5, depending on direction.

3. Component vs. Resultant
Component vectors are the individual parts (or vectors) that we consider acting at one point at a given time.
The resultant, or net vector, has the same effect as the combination of all component vectors, and therefore is equal to the sum of the components.

4. Let’s consider three different cases.
3 + 4 =
1 (left)
To find the magnitude of a resultant that is diagonal, you must use the Pythagorean Theorem.
The resultant will be the hypotenuse of a triangle: you must choose the right lengths for each leg.
Let’s have this point represent our starting location, our origin.
3 + 4 =
7 (right)
By now you may have noticed how we add one vector to another.
We start by choosing a starting vector, then redrawing the second vector onto the first.
3 + 4 =
5 (diagonally)
In our case, the length of the resultant is equal to or or 5

5. When adding multiple vectors…
Start with diagonal vectors (harder to re-draw)
Add 3rd vector to end of 2nd, 4th to end of 3rd, and so on.
To find the length of the resultant, then we must use Pythagorean Theorem.
We will find the legs which frame this hypotenuse and take the square root of the sum of the squares.
Therefore our answer will be…
= = units