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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 point A(1, 2, 3) with direction ratios (1, 2, 3).
💡 Hint: Use the formula \\( \\vec{r} = \\vec{a} + \\lambda \\vec{b} \\).
Question 2
Easy
What is the parametric equation of a line with point (0, 0, 0) and direction vector (1, 1, 1)?
💡 Hint: Remember to express each coordinate in terms of \\( \\lambda \\).
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
Which form expresses a line using a direction vector?
- Parametric Form
- Symmetric Form
- Vector Form
💡 Hint: Think about the way each form is structured.
Question 2
True or False: The parametric form can be used to find specific points on the line.
- True
- False
💡 Hint: Recall how we use \\( \\lambda \\) in those equations.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a point A(2, 3, 4) and direction ratios (1, -1, 2), write the equations in all three forms: vector, parametric, and symmetric.
💡 Hint: Use the initial point and direction ratios for conversions.
Question 2
Prove that the point (3, 4, 5) lies on the line defined by \( \frac{x-1}{2} = \frac{y+1}{-1} = \frac{z-2}{3} \).
💡 Hint: Verify each coordinate substitution against the symmetric definitions.
Challenge and get performance evaluation