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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the equation of a plane passing through the point (2, 3, 4) with a normal vector (1, 2, 3)?
💡 Hint: Use the equation format A(x - x₀) + B(y - y₀) + C(z - z₀) = 0.
Question 2
Easy
Identify the components of the normal vector for the equation 5(x - 1) + 2(y - 2) + 3(z - 3) = 0.
💡 Hint: The coefficients of (x, y, z) are the normal vector components.
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 normal vector represent in the plane equation?
- A point on the plane
- The plane's orientation
- The distance from the origin
💡 Hint: Remember the normal vector is always perpendicular to the plane.
Question 2
Is the equation of a plane unique for given point and normal vector?
- True
- False
💡 Hint: Consider whether changing the normal vector alters the plane.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the plane equation 2(x - 3) + 4(y + 1) - 5(z - 2) = 0, identify the normal vector of the plane.
💡 Hint: The coefficients of (x, y, z) give the components of the normal vector.
Question 2
Find the equation of a plane passing through points (1, 2, 3) and (3, 4, 5) with a normal vector calculated from these points.
💡 Hint: You might need to calculate the cross product to find a normal vector based on multiple points.
Challenge and get performance evaluation