Position Vectors (AQA A Level Maths: Pure)

What is a position vector?

• Position vectors describe the position of a point in relation to the origin
• They are different to displacement vectors which describe the direction and distance between any two points

 

Distance between two points

• The distance between two points is the magnitude of the vector between them (see Magnitude Direction)

 

How do I find the magnitude of a displacement vector?

• You can use coordinate geometry to find magnitudes of displacement vectors from A  to B
  • From the position vectors of A  and B  you know their coordinates
    • If  ,  then point A has coordinates
    • If  ,  then point B has coordinates 
  • The distance between two points is given by 
    • So 
  • For example, if points A and B have position vectors  and  respectively
    • then  

• Alternatively, you could find  by
  • first using  to find in vector form
    • and then calculating its magnitude directly
  • See the Worked Example below