## 2.3 Vector arithmetic and algebra

### 2.3.1 Scalar multiplication

#### Example

You may use the interactive below to observe how scalar multiplication works. You can adjust the *x* and *y *components of the vector, and also adjust the scalar *c*. After playing around with the interactive to get a sense of how it works, you should make some predictions: write down a vector on a piece of paper, and multiply it by some scalar. Then check your answer using the interactive.

#### Practice

### 2.3.2 Vector addition and subtraction

You will frequently need to add vectors together. There are two methods of adding vectors: graphically and algebraically.

#### Graphically

Place the “tail” of one vector at the origin. Place the “tail” of the other at the “tip” of the first. The sum of the two is the vector that points from the “tail” of the first vector to the “tip” of the second.

For subtraction, keep the magnitude (length) the same, but put it in the opposite direction.