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IBMathsDPApplications & Interpretation (AI)HLRevision Notes3. Geometry & TrigonometryVector Equations of LinesEquation of a Line in Parametric Form

Equation of a Line in Parametric Form (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): HLDP Analysis & Approaches (AA): HLDP Applications & Interpretation (AI): HL

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Equation of a Line in Parametric Form

What is the equation of a line in parametric form?

  • The parametric form of the equation of a line is:

    • x equals x subscript 0 plus lambda l blank

    • y equals y subscript 0 plus lambda m

    • z equals z subscript 0 plus lambda n

  • open parentheses x subscript 0 comma space y subscript 0 comma space z subscript 0 close parentheses is the coordinates of any point on the line

  • The vector l bold italic i plus m bold italic j plus n bold italic k is a direction vector of the line

Examiner Tips and Tricks

This is given in the formula booklet under the geometry and trigonometry section. However, you need to remember what the components represent.

  • You can write it easily in its vector form bold italic r equals bold italic a plus lambda bold italic b

    • begin mathsize 16px style open parentheses fraction numerator x over denominator table row y row z end table end fraction close parentheses equals blank open parentheses fraction numerator x subscript 0 over denominator table row cell y subscript 0 end cell row cell z subscript 0 end cell end table end fraction close parentheses plus lambda open parentheses fraction numerator l over denominator table row m row n end table end fraction close parentheses end style

      • bold italic r equals blank open parentheses fraction numerator x over denominator table row y row z end table end fraction close parentheses

      • bold italic a equals open parentheses fraction numerator x subscript 0 over denominator table row cell y subscript 0 end cell row cell z subscript 0 end cell end table end fraction close parentheses

      • bold italic b equals open parentheses fraction numerator l over denominator table row m row n end table end fraction close parentheses

Worked Example

Write the parametric form of the equation of the line which passes through the point (-2, 1, 0) with direction vector begin mathsize 16px style open parentheses fraction numerator 3 over denominator table row 1 row cell negative 4 end cell end table end fraction close parentheses end style.

3-10-1-ib-aa-hl-parametric-we

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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.