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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
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} \\).
Question 2
Easy
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the Symmetric Form of a line in 3D?
- A representation using midpoints
- An equation combining coordinates and direction ratios
- A method to find angles alone
💡 Hint: Think about what ratios represent in relations to lines.
Question 2
True or False: The Symmetric Form can be used to determine if two lines are parallel.
- True
- False
💡 Hint: What do direction ratios tell us about lines?
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation