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IBMathsDPAnalysis & Approaches (AA)HLRevision Notes3. Geometry & TrigonometryVector PropertiesParallel Vectors

Parallel Vectors (DP IB Analysis & Approaches (AA)): Revision Note

Amber

Written by: Amber

Reviewed by: Dan Finlay

Updated on

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

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Parallel Vectors

How can I tell if two vectors are parallel?

  • Two vectors are parallel if one is a scalar multiple of the other

    • This means that all components of the vector have been multiplied by a common constant (scalar)

    • For example, open parentheses table row 1 row 0 row 3 end table close parentheses and open parentheses table row 2 row 0 row 6 end table close parentheses are scalar multiples

  • Multiplying the components of a vector by a positive scalar changes the magnitude of the vector but not the direction

    • For example, open parentheses table row 2 row 0 row 6 end table close parentheses is double the length of open parentheses table row 1 row 0 row 3 end table close parentheses but in the same direction

  • Multiplying the components of a vector by a negative scalar reverses the direction

  • You can factorise a vector to help spot if two vectors are parallel

    • 9 bold italic i plus 6 bold italic j – 3 bold italic k equals 3 open parentheses 3 bold italic i plus 2 bold italic j minus bold italic k close parentheses

    • negative 6 bold italic i minus 4 bold italic j plus 2 bold italic k equals negative 2 open parentheses 3 bold italic i plus 2 bold italic j minus bold italic k close parentheses

      • They are scalar multiples of the same vector so they are parallel

Diagram illustrating parallel vectors with examples using scalars. Includes vector equations, rules for column and i/j vectors, and a parallelogram ABCD.
Example of parallel vectors

Examiner Tips and Tricks

If you are told that two vectors (bold italic a and bold italic b) are parallel, then it can be helpful to define a scalar to form an equation bold italic a equals k bold italic b .

Worked Example

Show that the vectors bold italic a equals open parentheses table row 2 row 0 row cell negative 4 end cell end table close parentheses and bold italic b equals negative 3 bold italic i plus 6 bold italic k are parallel and find the scalar multiple that maps bold italic a onto bold italic b.

3-9-2-ib-aa-hl-parallel-vectors-we-solution

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    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.