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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the coordinates of the point that divides the segment joining (0, 0, 0) and (2, 2, 2) in the ratio 1:2.
💡 Hint: Apply the section formula using the given coordinates.
Question 2
Easy
What is the ratio for a point that equally divides the segment between (3, 3, 3) and (4, 4, 4)?
💡 Hint: Think about equal division.
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 section formula in three dimensions calculate?
- The area of a triangle
- Coordinates of a dividing point
- Distance between two points
💡 Hint: Think about dividing segments in geometry.
Question 2
The coordinates (5, 6, 7) divide the segment from (2, 3, 4) to (8, 9, 10) in what ratio?
💡 Hint: Use the section formula to relate coordinates to ratio.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider points A(3, 2, 1) and B(7, 8, 5), a point divides the line segment AB externally in the ratio 4:3. Calculate the coordinates of the dividing point.
💡 Hint: Refer to the section formula that accounts for external division.
Question 2
Two points P(-5, -2, -3) and Q(5, 3, 7) create a segment divided by a point R in ratio 2:-1. Find the coordinates of point R.
💡 Hint: The formula needs adjusting for negative ratios in external division.
Challenge and get performance evaluation