IGCSEMathsEdexcelMaths A (Modular)Higher Unit 2Revision NotesVectors & Transformation GeometryVectorsPosition & Displacement Vectors

Position & Displacement Vectors (Edexcel IGCSE Maths A (Modular))

Revision Note

Flashcards
Mark Curtis

Expertise

Maths

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.

Exam Tip

  • 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

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    Mark Curtis

    Author: Mark Curtis

    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.