IGCSEMathsCambridge (CIE)ExtendedRevision NotesVectors & TransformationsVectorsPosition & Displacement Vectors

Position & Displacement Vectors (Cambridge (CIE) IGCSE Maths) : Revision Note

Mark Curtis

Written by: Mark Curtis

Reviewed by: Dan Finlay

Updated on

Cambridge (CIE) Maths: ExtendedEdexcel Maths A (Modular): Higher Unit 2Edexcel Maths A: Higher

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 = stack O A with rightwards arrow on top  

  • Their components are equal to their coordinates

    • The point with coordinates (3, -2) has position vector open parentheses table row 3 row cell negative 2 end cell end table close parentheses 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 stack A B with rightwards arrow on top

      • 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)

      • stack A B with rightwards arrow on top equals negative bold a plus bold b equals bold b minus bold a

      • This is a useful rule to remember

Diagram explaining displacement vector AB. Position vectors of points A and B are given as a and b, respectively. AB=b−a, indicating route via point O.

Examiner Tips and Tricks

  • You may need to draw an origin, O , on to a diagram to be able to sketch position vectors.

Worked Example

The points P and Q have position vectors open parentheses table row 3 row 2 end table close parentheses and open parentheses table row 6 row cell negative 10 end cell end table close parenthesesrespectively.

Find and simplify the vector stack P Q with rightwards arrow on top.

Let bold p and bold q be position vectors of P  and Q
stack P Q with rightwards arrow on top is the displacement vector from P  to Q
Use the rule that stack A B with rightwards arrow on top equals negative bold a plus bold b equals bold b minus bold a

stack P Q with rightwards arrow on top equals bold q minus bold p

Substitute in bold p and bold q

stack P Q with rightwards arrow on top equals open parentheses table row 6 row cell negative 10 end cell end table close parentheses minus open parentheses table row 3 row 2 end table close parentheses

Expand and simplify

table row blank equals cell open parentheses table row cell 6 minus 3 end cell row cell negative 10 minus 2 end cell end table close parentheses end cell row blank equals cell open parentheses table row 3 row cell negative 12 end cell end table close parentheses end cell end table

stack bold italic P bold italic Q with bold rightwards arrow on top bold equals stretchy left parenthesis table row 3 row cell negative 12 end cell end table stretchy right parenthesis

You can also get this answer by seeing what vector must be added to bold p to get bold q

👀 You've read 1 of your 5 free revision notes this week
An illustration of students holding their exam resultsUnlock more revision notes. It's free!

By signing up you agree to our Terms and Privacy Policy.

Already have an account? Log in

Test yourselfFlashcards

Did this page help you?

Previous:Magnitude of a VectorNext:Finding Vector Paths
Author
Reviewer
Mark Curtis

Author: Mark Curtis

Expertise: Maths Content Creator

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

Download notes on Position & Displacement Vectors