Scalar and Vector Quantities

Aim: Resolve, add and subtract vectors in one plane

A scalar is any quantity with a magnitude, but no direction.

A vector is any quantity with both magnitude and direction.
Vectors can be represented as follows to distinguish between the two:


Vectors are represented by a line with an arrow:


Length= magnitude; angle = direction


Expressed in full circle bearing (true bearing), a clockwise angle from north


Expressed as a quadrant bearing, the angle between two cardinal directions and the line

Vector Components

It is possible to represent a vector by splitting it into two perpendicular components. (Usually vertical and horizontal).

 vector addition
Vector Scaling

Multiplying a vector multiples the magnitude but does not change the direction.

If multiplied by a negative, the direction is reversed.

Vector Addition


  1. Draw a reference frame
  2. Draw the first vector
  3. Draw the second vector, so that the start of the second vector is the head of the first
  4. Repeat for all n vectors
  5. Draw the resultant vector from the tail of the first vector to the head of the last one.

Note that this should be to scale.


  1. Calculate the perpendicular components of each vector
  2. Add similar components of the different vectors (add horizontal to horizontal etc.)
  3. Using the new values, draw a vector diagram
  4. Use Pythagoras and trigonometry to determine the resultant vector

Vector Subtraction

Subtracting by a vector is the same as adding its negative.

That is

  vector subtraction = fa – fb

                                     = fa + (-fb)

  1. Flip the vector you are subtracting by. Magnitude remains the same, but direction is reversed
  2. The rest is the same as vector addition

You may also like...

Leave a Reply

%d bloggers like this: