Scalars and Vectors:

 

Scalar quantities:

A scalar quantity is a magnitude (size) value only

E.g.      Mass

            Temperature

            Area

Volume

Vector quantities:

Vector quantities have both size and direction

E.g.      Force

            Weight

            Velocity

            Acceleration

 Vector quantities can be expressed by arrows whose length represents the magnitude and direction is the direction of the vector quantity. 

 Adding vectors:

Vectors can be added diagrammatically by placing the vectors head to tail giving a resultant vector from the start of the first to the end of the last.

 The best way to show a worked example of how to add vectors is by an example:

 

 

 

 

The box above has a force of 2 Newtons pushing it left and a force of 3 Newtons pushing it up we can add these forces together

 

 

 

 

The red line is the resultant force we add the two forces by using Pythagoras.

 Resultant = √22+32

                    = √13

                =  3.6

 We work out the angle of the force by using trigonometry: 

θ = tan-1 1.5

    = 56.3°

 So vector = 3.61 N at an angle of 56.3° to the horizon 

All vectors can be added in a similar fashion.

 Resolving vectors:

 Any vector can be resolved into its components.  This is shown below:

  Above vector V is split into two perpendicular components Vx and Vy so

V  =  Vx  +  Vy

 Example:

 

 Vx = V sin θ

Vy = V cos θ

 Vx = 16 sin 30

     = 13.86 N

Vy = 16 cos 30

     = 8 N