5.3 - Symmetric 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 symmetric form for the line passing through (1, 2, 3) with direction ratios (4, 5, 6).
💡 Hint: Use the structure \\( \\frac{x - x_1}{a} = \\frac{y - y_1}{b} = \\frac{z - z_1}{c} \\).
What are the direction ratios of the line given by the symmetric form: (x-1)/3 = (y-4)/2 = (z-5)/1?
💡 Hint: Identify the numbers in the denominator of the ratios.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the Symmetric Form of a line in 3D?
💡 Hint: Think about what ratios represent in relations to lines.
True or False: The Symmetric Form can be used to determine if two lines are parallel.
💡 Hint: What do direction ratios tell us about lines?
1 more question available
Challenge Problems
Push your limits with advanced challenges
Identify if the following lines represented by their symmetric forms intersect: A: (x-1)/2 = (y+3)/3 = (z-4)/1 and B: (x+2)/2 = (y-5)/-1 = (z+1)/0.
💡 Hint: Align the equations correctly.
Determine the angle between two lines expressed in symmetric forms: A: (x-1)/1 = (y-2)/2 = (z-3)/-3 and B: (x+3)/3 = (y-1)/1 = (z+2)/1.
💡 Hint: Remember the angle can be determined using cosines via direction ratios.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.