### What are Scalar & Vector Quantities?

- A
**scalar**is a quantity which**only**has a magnitude (size) - A
**vector**is a quantity which has**both**a magnitude and a direction - For example, if a person goes on a hike in the woods to a location which is a couple of miles from their starting point
- As the crow flies, their
**displacement**will only be a few miles but the**distance**they walked will be much longer

- As the crow flies, their

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

**Distance**is a scalar quantity because it describes how an object has travelled overall, but not the direction it has travelled in**Displacement**is a vector quantity because it describes how far an object is from where it started and in what direction- There are a number of common scalar and vector quantities

** Scalars and Vectors Table**

#### Exam Tip

Do you have trouble figuring out if a quantity is a vector or a scalar? Just think – can this quantity have a minus sign? For example – can you have negative energy? No. Can you have negative displacement? Yes!

### Combining Vectors

**Vectors**are represented by an arrow- The arrowhead indicates the
**direction**of the vector - The length of the arrow represents the
**magnitude**

- The arrowhead indicates the
- Vectors can be combined by
**adding**or**subtracting**them from each other - There are two methods that can be used to combine vectors: the
**triangle method**and the**parallelogram method** - To combine vectors using the 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

- To combine vectors using the 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

- When two or more vectors are added together (or one is subtracted from the other), a single vector is formed and is known as the
**resultant**vector

### Resolving Vectors

- Two vectors can be represented by a single
**resultant vector**that has the same effect - A single resultant vector can be resolved and represented by
**two**vectors, which in combination have the same effect as the original one - When a single resultant vector is broken down into its
**parts**, those**parts**are called components - For example, a force vector of magnitude
*F*and an angle of*θ*to the horizontal is shown below