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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

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Equation of a Line in Parametric Form

How do I find the vector equation of a line in parametric form?

  • By considering the three separate components of a vector in the x, y and z directions it is possible to write the vector equation of a line as three separate equations

    • Letting begin mathsize 16px style bold italic r equals blank open parentheses fraction numerator x over denominator table row y row z end table end fraction close parentheses end style then bold italic r equals bold italic a plus lambda bold italic b becomes

    • 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

      • Where begin mathsize 16px style 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 end style is a position vector and begin mathsize 16px style open parentheses fraction numerator l over denominator table row m row n end table end fraction close parentheses end style is a direction vector

    • This vector equation can then be split into its three separate component forms:

      • x equals blank x subscript 0 plus blank lambda l blank

      • y equals blank y subscript 0 plus blank lambda m blank

      • z equals blank z subscript 0 plus blank lambda n

    • These are given in the formula booklet

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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    Amber

    Author: Amber

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    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.