IGCSEMathsEdexcelMaths BRevision NotesVectors & Transformation GeometryVectorsModulus of a Vector

Modulus of a Vector (Edexcel IGCSE Maths B): Revision Note

Exam code: 4MB1

Jamie Wood

Written by: Jamie Wood

Reviewed by: Roger B

Updated on

Edexcel Maths BEdexcel Maths A (Modular): Higher Unit 2Edexcel Maths A: HigherCambridge (CIE) International Maths: ExtendedCambridge (CIE) Maths: Extended

Modulus (magnitude) of a vector

How do I find the modulus of a vector?

  • The modulus of a vector is its length (distance)

    • It is sometimes also called the magnitude

    • This is always a positive value

    • The direction of the vector is irrelevant

  • The modulus of stack A B with italic rightwards arrow on top is written open vertical bar stack A B with rightwards arrow on top close vertical bar

    • The modulus of a is written |a|

  • Depending on the use of the vector, the modulus of a vector represents different quantities

    • For velocity, modulus would be speed

    • For a force, modulus would be the strength of the force (in Newtons)

  • In component form, the modulus is the hypotenuse of a right-angled triangle

    • Use Pythagoras' theorem to find the modulus

    • The modulus of bold a equals blank open parentheses table row x row y end table close parentheses

      • is open vertical bar bold a close vertical bar equals blank square root of x to the power of 2 space end exponent plus blank straight y squared end root

Diagram showing a vector P with horizontal component x and vertical component y. The magnitude of the vector is |P|.

Examiner Tips and Tricks

If there is no diagram, sketch one!

You can sketch a vector and use it to form a right-angled triangle.

Worked Example

Consider two points A open parentheses negative 3 comma space 5 close parentheses and B open parentheses 7 comma space 1 close parentheses.

(a) Write down the column vector stack A B with rightwards arrow on top.

Answer:

Find the horizontal and vertical distances between the two points
Subtract the x and y components of A from B

stack A B with rightwards arrow on top equals open parentheses table row cell 7 minus negative 3 end cell row cell 1 minus 5 end cell end table close parentheses

stack A B with italic rightwards arrow on top equals stretchy left parenthesis table row 10 row cell negative 4 end cell end table stretchy right parenthesis

(b) Find the modulus of vector stack A B with rightwards arrow on top.

Answer:

Sketching a diagram of the vector stack A B with rightwards arrow on top can help

Right-angled triangle formed from points A and B. The horizontal distance is 10, the vertical distance is 4 and the hypotenuse is the magnitude of the vector from A to B.

Apply Pythagoras' theorem to the x and y components of stack A B with rightwards arrow on top

table row cell open vertical bar stack A B with rightwards arrow on top close vertical bar end cell equals cell square root of 10 squared plus open parentheses negative 4 close parentheses squared end root end cell row blank equals cell square root of 100 plus 16 end root end cell row blank equals cell square root of 116 end cell end table

Error converting from MathML to accessible text.

(c) Briefly explain why open vertical bar stack B A with rightwards arrow on top close vertical bar equals open vertical bar stack A B with rightwards arrow on top close vertical bar.

Answer:

The modulus of a vector is it's 'size'

Direction of the vector is ignored

open vertical bar stack B A with rightwards arrow on top close vertical bar equals open vertical bar stack A B with rightwards arrow on top close vertical bar since both vectors have the same length

(d) Another vector, stack C D with rightwards arrow on top, has three times the modulus of vector stack A B with rightwards arrow on top.

Write down a possible column vector for stack C D with rightwards arrow on top.

Answer:

Being three times open vertical bar stack A B with rightwards arrow on top close vertical bar means the vector stack A B with rightwards arrow on top is three times longer

One way to find a vector is to multiply each component of the vector stack A B with rightwards arrow on top by 3 or -3

table row cell stack C D with rightwards arrow on top end cell equals cell 3 stack A B with rightwards arrow on top equals 3 open parentheses table row 10 row cell negative 4 end cell end table close parentheses end cell end table

stack C D with italic rightwards arrow on top equals stretchy left parenthesis table row 30 row cell negative 12 end cell end table stretchy right parenthesis

Another possible answer is stack C D with italic rightwards arrow on top equals stretchy left parenthesis table row cell negative 30 end cell row 12 end table stretchy right parenthesis

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Previous:Representing Vectors as DiagramsNext:Position & Displacement Vectors
    Author
    Reviewer
    Jamie Wood

    Author: Jamie Wood

    Expertise: Maths Content Creator

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

    Roger B

    Reviewer: Roger B

    Expertise: Maths Content Creator

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.