Position Vectors (AQA AS Maths): Revision Note

Position Vectors

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