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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What are direction ratios and why are they important?
💡 Hint: Think about how they relate to direction cosines.
Question 2
Easy
Use the direction ratios (1, 1, 1) and (2, 2, 2) to find the angle between the lines.
💡 Hint: What does it mean when ratios are proportional?
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 are direction ratios used for in three-dimensional geometry?
- To describe lines
- To calculate areas
- To measure distances
💡 Hint: Think about how they define a line's slope or direction.
Question 2
True or False: The angle between two lines can also be determined from their direction cosines.
- True
- False
💡 Hint: Relate it to how angles are calculated.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Calculate the angle between the line passing through the points (1, 2, 3) and (2, 3, 4) with the line represented by direction ratios (4, 0, -4).
💡 Hint: Form the vector, simplify the direction ratios, and apply the cosine formula.
Question 2
Prove if the lines (3, 2, 5) and (1, -1, -1) are perpendicular by checking the angle between them.
💡 Hint: Focus on the numerator of the cosine formula.
Challenge and get performance evaluation