IBMathsDPAnalysis & Approaches (AA)HLRevision Notes3. Geometry & TrigonometryVector Equations of LinesEquation of a Line in Parametric Form

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

Did this video help you?

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
👀 You've read 1 of your 5 free revision notes this week
An illustration of students holding their exam resultsUnlock more revision notes. It’s free!

By signing up you agree to our Terms and Privacy Policy.

Already have an account? Log in

Test yourself

Did this page help you?

Previous:Equation of a Line in Vector FormNext:Equation of a Line in Cartesian Form
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.

Download notes on Equation of a Line in Parametric Form