Practice - Equation of a Line in 3D
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Practice Questions
Test your understanding with targeted questions
What are the parametric equations of a line through point A(0, 0, 0) with direction vector (1, 1, 1)?
💡 Hint: Remember to express each coordinate with respect to the parameter 't'.
What is the symmetric form for the line defined by the parametric equations x = 2 + 3t, y = 5 + 6t, z = 7 + 8t?
💡 Hint: Convert each equation back to express the ratio.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the first step to write the parametric form of a line?
💡 Hint: Think about what you need to define a path in space.
True or False: The symmetric form can be used when any part of the direction vector is zero.
💡 Hint: Consider the implications of zero in ratios.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given two points F(1, 2, 3) and G(-1, -2, -4), write the line equation in both parametric and symmetric forms and explain any assumptions if one direction vector component is zero.
💡 Hint: Remember, how does zero in a vector change the representation?
Find the distance between two lines defined by their equations: L1: (x - 2)/1 = (y - 3)/2 and L2: (x - 4)/-1 = (y + 1)/3. Are they parallel?
💡 Hint: What defines parallelism in lines?
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