# Vectors and scalars

## Scalar

Scalar – Quantity having only magnitude (not direction). It’s only a number.

The **scales (scalar)** only give you a number.

Scalar quantities include:

- Speed
- Area
- Value
- Temperature
- Distance
- Time
- Mass

To name but a few.

All these examples only have size (magnitude). Unlike a vector, it doesn’t mention direction.

Scalars are easy to use. You just add the numbers.

**Example 1**

3m |
+ |
4m |
= |
7m |

Area |
+ |
Area |
= |
Area |

**Example 2**

A person buys a bag of sugar labelled with a mass of 500g. The mass of this bag of sugar is a scalar quantity. It only needs a number to describe it.

## Vector

Vector – Is a line which has magnitude (how long it is) and direction.

They drove the convector for a long period of time (how long) northwards (and direction).

A vector is a physical quantity that has both a magnitude and a direction

**Examples of vectors:**

- Velocity (speed and direction)
- Displacement (distance in a given direction)
- Force (you push something with strength (magnitude) in a particular direction e.g. up a hill)
- Acceleration (is a vector quantity because it has both magnitude and direction. When an object has a positive acceleration, the acceleration occurs in the same direction as the movement of the object. When an object has a negative acceleration (it's slowing down) the acceleration occurs in the opposite direction to the movement of the object).

**Example 1**

A car travels at 70mph in the direction of East. We know the magnitude which is 70mph and going East is the direction. Speed (magnitude) and direction together form a vector we call velocity.

**Example 2**

John walks north 20 metres. The direction”north” together with the distance “20 metres” is a vector called displacement.

**Example 3**

Vectors can be added or subtracted from each other to produce a resultant vector.

If you were stood at the intersection of the x, y and z axis in the image above the person in the image is at a displacement from the tree. This displacement is equal to the tree's displacement position from you, minus the person's displacement position from you.

**Example 4**

It does not matter which order you add vectors together. The resultant vector will be the same.

If you add vector a (blue vector) to vector b (red vector) the resultant green vector will be the same as if you added vector b (red vector) to vector a (blue vector).

**Example 5**

An apple falls down at 10 metres per second. The direction “down” combined with the speed “10 metres per second” is a vector (this kind of vector is called velocity).