5.2 - Parametric Form
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Write the parametric equations for a line that passes through (2, 3, 4) with direction ratios (1, 2, 3).
💡 Hint: Use the point and direction ratios to construct the equations.
If λ = 2 for the previous equations, what are the coordinates?
💡 Hint: Substitute λ into your parametric equations.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the meaning of the parameter λ in parametric equations?
💡 Hint: Think about how λ controls the points on the line.
True or False: The parametric equations for a line in space can be used to find the coordinates of any point on the line.
💡 Hint: Recall how changing λ affects point locations.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Find the parametric equations of a line if it passes through (2, 3, 4) and is parallel to the vector (1, 2, 1).
💡 Hint: Start with the point coordinates and add the direction ratios scaled by λ.
Two lines are parametrically defined as L₁: (x, y, z) = (1 + t, 2 + 2t, 3 + 3t) and L₂: (x, y, z) = (4 - s, 5 - 2s, 6 + s). Determine if these lines intersect.
💡 Hint: Formulate a system of equations and check for solutions.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.