 # 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 just add the numbers

Example 1

 3m2 + 4m2 = 7m2 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 con vector 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 say 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 (its slowing down) the acceleration occurs in the opposite direction as the movement of the object).

Example 1

If a car travels at 70mph in the direction of East. We know the magnitude which is 70mph and going East is the direction. Speed and direction of the car (magnitude and a 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 trees displacement position from you, minus the persons 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).