Position & Displacement Vectors (Edexcel IGCSE Maths B): Revision Note

Position & displacement vectors

What are position vectors?

• A position vector describes where a specific point, A , is, relative to a fixed origin, O

  • Lower-case bold (or underlined) letters are used

    • The point A  has position vector a = $\overrightarrow{OA}$  

• Their components are equal to their coordinates

  • The point with coordinates (3, -2) has position vector $\left(\begin{array}{c}3\\ -2\end{array}\right)$ from the origin

What are displacement vectors?

• A displacement vector describes the direction and distance between two points

  • The displacement vector from A  to B  is $\overrightarrow{AB}$

    • How to get from A  to B

• If the points A  and B  have position vectors a and b relative to O 

  • then A  to B  is the same as A  to O  (-a) followed by O  to B  (b)

    • $\overrightarrow{AB}=-\mathbf{a}+\mathbf{b}=\mathbf{b}-\mathbf{a}$

    • This is a useful rule to remember