Position & Displacement Vectors (DP IB Analysis & Approaches (AA)): Revision Note

A position vector describes the position of a point in relation to the origin

The position vector of point A is written with the notation  

• The origin is always denoted O

The individual components of a position vector are the coordinates of the point

• For example, the point with coordinates (3, -2, -1) has position vector

A displacement vector describes the shortest route between any two points

The displacement vector of point B from the point A is written with the notation 

A position vector is a displacement vector of a point from the origin

A displacement vector between two points can be written in terms of the displacement vectors using a third point

• For example,

A displacement vector can be written in terms of its position vectors

•  For example, can be written in terms of  and 

  • 

  • This can be rewritten as