Revision NotesExam QuestionsFlashcardsPast PapersMock Exams
IBMathsDPApplications & Interpretation (AI)HLRevision Notes3. Geometry & TrigonometryVector PropertiesMagnitude of a Vector & Unit Vectors

Magnitude of a Vector & Unit Vectors (DP IB Applications & Interpretation (AI)): Revision Note

Amber

Written by: Amber

Reviewed by: Dan Finlay

Updated on

DP Applications & Interpretation (AI): HLDP Analysis & Approaches (AA): HL

Did this video help you?

Magnitude of a Vector

What is the magnitude of a vector?

  • The magnitude of a vector tells us its length

    • The magnitude of a displacement vector is the distance between the two points

    • The magnitude of a position vector is the distance of the point from the origin

  • The magnitude of the vector is denoted by two vertical lines around the vector

    • For example, the magnitude of the vector a is denoted |a|

How do I find the magnitude of a vector?

  • The magnitude of a vector can be found using Pythagoras’ theorem

  • The formula for the magnitude of a vector is open vertical bar bold italic v close vertical bar equals blank square root of v subscript 1 superscript space 2 end superscript plus blank v subscript 2 superscript blank 2 end superscript plus v subscript 3 superscript blank 2 end superscript end root

    • bold italic v equals blank open parentheses table row cell v subscript 1 over v subscript 2 end cell row cell v subscript 3 end cell end table close parentheses

Examiner Tips and Tricks

This is given in the formula booklet under the geometry and trigonometry section. As you are squaring each component, you can ignore the negative signs.

Vectors in 3 Dimensions Diagram 2a, AS & A Level Maths revision notes

How do I find the distance between two points using vectors?

  • STEP 1
    Find the displacement vector between them

  • STEP 2
    Find the magnitude of the displacement vector

Examiner Tips and Tricks

If you label the points open parentheses x subscript 1 comma space y subscript 1 comma space z subscript 1 close parentheses and open parentheses x subscript 2 comma space y subscript 2 comma space z subscript 2 close parentheses, then you get the same formula using the Cartesian coordinates d equals square root of open parentheses x subscript 1 minus x subscript 2 close parentheses squared plus open parentheses y subscript 1 minus y subscript 2 close parentheses squared plus open parentheses z subscript 1 minus z subscript 2 close parentheses squared end root.

Worked Example

Find the magnitude of the vector AB with rightwards arrow on top space equals 4 bold italic i – bold italic j plus 2 bold italic k.

3-9-3-ib-aa-hl-magnitude-we-solution-a

Did this video help you?

Unit Vectors

What is a unit vector?

  • A unit vector has a magnitude of 1

  • You can find a unit vector that is in the same direction as the vector bold italic a by dividing the components of the vector by the magnitude of the vector

    • fraction numerator bold italic a over denominator open vertical bar bold italic a close vertical bar end fraction is a unit vector in the direction of bold italic a

    • For example, a unit vector in the direction 3 bold italic i – 4 bold italic j is fraction numerator 1 over denominator square root of 3 squared plus 4 squared end root end fraction left parenthesis 3 bold italic i minus 4 bold italic j right parenthesis equals 3 over 5 bold italic i minus 4 over 5 bold italic j

Examiner Tips and Tricks

It is unlikely that an exam question will ask you to find a unit vector. However, it is helpful to understand what they are.

Worked Example

Find the unit vector in the direction 2 bold italic i – 2 bold italic j plus bold italic k.

3-9-3-ib-aa-hl-magnitude-we-solution-b

You've read 0 of your 5 free revision notes this week

Unlock more, it's free!

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

the (exam) results speak for themselves:

    Test yourselfFlashcards

    Did this page help you?

    Previous:Position & Displacement VectorsNext:The Scalar Product
    Author
    Reviewer
    Amber

    Author: Amber

    Expertise: Maths Content Creator

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

    Dan Finlay

    Reviewer: Dan Finlay

    Expertise: Maths Subject 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.