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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
State the relationship between direction cosines and direction ratios.
💡 Hint: Think about how direction ratios are derived.
Question 2
Easy
What is the sum of the squares of direction cosines?
💡 Hint: Recall the equation that defines the direction cosines.
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 do direction cosines represent?
- Angles a line makes with axes
- Length of a line
- Direction ratios
💡 Hint: Think about the term 'cosine' in relation to angles.
Question 2
True or False: Direction ratios must always sum to one.
- True
- False
💡 Hint: What property is unique to direction cosines?
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given points A(2, 3, 4) and B(5, 6, 7), derive the direction cosines and ratios, then find the angle they create with each axis.
💡 Hint: Focus on the differences first—this will lead you to your direction cosines.
Question 2
If a line has a direction ratio of (3, 4, 0), calculate the angle it makes with the X and Y axes.
💡 Hint: Remember that angles can be found with the cosine of the direction cosine values.
Challenge and get performance evaluation