Introducing Vectors

A vector is a directed line segment - a line with an arrow head at the end indicating a direction


When writing a symbol to represent a vector quantity  we place an arrow on top of the symbol.

This method serves to distinguish the symbol from its scalar counterpart.

The symbol for displacement is

d vector

noteNote that displacement is  a vector quantity whereas distance is not.  

  • The standard SI (System International) unit for displacement is the meter (m). 
  • The symbol for distance is d (no arrow means "scalar quantity").

If we say that to go to your friend's house you need to walk ten steps then we really don't know in which direction you need  to take ten steps to go to her house.  This defines the distance (just the quantity of steps) you need to walk and therefore it is a "scalar" quantity.

If instead we say that your friend lives ten steps south of your house then you have given us a direction.  You will need to walk 10 steps in a southerly direction to go visit her.  You have therefore defined a vector quantity which has magnitude (10 steps) and a direction (south).

note To make things simpler we will omit placing arrows on symbols to indicate vectors. Instead we will use characters in "bold"  typeface  to represent vectors.

Therefore,  instead of d vector we will write d.