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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Calculate the distance between points (0, 0, 0) and (3, 4, 5).
💡 Hint: Use the distance formula.
Question 2
Easy
Determine if points (1, 2, 3), (2, 4, 6), and (3, 6, 9) are collinear.
💡 Hint: Check if they lie on the same line.
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 distance between points (1,1,1) and (4,5,9)?
- 8.24
- 7.14
- 9.54
💡 Hint: Apply the distance formula and calculate each component.
Question 2
True or False: The points (1, 0, 0), (2, 0, 0), and (3, 0, 0) define a unique plane.
- True
- False
💡 Hint: Consider the definition of collinearity.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given points A(1, 1, 0), B(2, 2, 1), and C(3, 3, 2), determine if these points span a plane. If so, find its equation.
💡 Hint: Calculate the vectors between the points.
Question 2
Points A(1, 2, 3), B(4, 5, 6), and C(7, 8, 9) are given. Show that these points do not lead to a valid plane equation.
💡 Hint: Check if the cross product of the two vectors yields non-zero results.
Challenge and get performance evaluation