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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Write the vector form of a line passing through the point (3, 2, 5) with a direction vector (1, 1, 1).
💡 Hint: Use the formula **r** = **a** + λ**b**.
Question 2
Easy
What is the position vector of the point (4, -2, 6)?
💡 Hint: Identify the coordinates as components of the position vector.
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 does the vector form of a line represent in 3D space?
- Position only
- Direction only
- Both position and direction
💡 Hint: Think about what information is needed to define a line in space.
Question 2
True or False: The direction vector can only change the length of the line.
- True
- False
💡 Hint: Recall the role of direction vectors in geometry.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Derive the symmetric form of a line given in vector form r = (2, 3, 4) + λ(1, -1, 2).
💡 Hint: Isolate λ in each component of the vector form.
Question 2
Prove whether the lines r1 = (1, 1, 1) + λ(2, 2, 2) and r2 = (3, 3, 3) + μ(4, 4, 4) intersect or are parallel.
💡 Hint: Consider the relationship between direction and parallel lines.
Challenge and get performance evaluation