### What are Scalar and Vector Quantities?

- A scalar is a quantity which only has magnitude, while a vector is a quantity which has both magnitude and direction
- For example, say you go on a hike in the woods to a location which is a couple of miles from your start point. As the crow flies, your displacement will only be a few miles but the distance you walked will be much longer

*Displacement is a vector while distance is a scalar quantity*

- Distance is a scalar quantity because it describes how far you have travelled overall but not the direction. Whereas displacement is a vector quantity because it tells you how far you are from where you started and in what direction.
- The table shows a variety of scalar and vector quantities you will come across in Physics:

### Combining Vectors

- Vectors are represented by an arrow to indicate its direction and length to represent its magnitude
- We can combine vectors by adding or subtracting them from each other
- There are two methods you can use to combine vectors: the triangle method and the parallelogram method
- Triangle method:
- Step 1: link the vectors head-to-tail
- Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector

- Parallelogram method
- Step 1: link the vectors tail-to-tail
- Step 2: complete the resulting parallelogram
- Step 3: the resultant vector is the diagonal of the parallelogram

#### Vector addition

#### Vector subtraction

#### Condition for equilibrium

*If three forces acting on an object are in equilibrium; they form a closed triangle*