Practice Normal Form - 8.3 | 6. Three Dimensional Geometry | ICSE 12 Mathematics
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Normal Form

8.3 - Normal Form

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define direction cosines in the context of a plane.

💡 Hint: Consider the definition of angles in relation to the coordinate axes.

Question 2 Easy

What is the equation of a plane in normal form?

💡 Hint: Recall the components of the normal form and its variables.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the normal form of a plane describe?

Distance from the plane
Orientation of the plane
Both A and B

💡 Hint: Think about all components mentioned in the normal form.

Question 2

True or False: The normal vector is the same as the direction vector.

True
False

💡 Hint: Recall their definitions and functions in geometry.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

A plane is defined by the point (3, 4, 5) and normal vector (1, 2, 3). Determine the normal form of this plane.

💡 Hint: Substitute the point into the normal form structure.

Challenge 2 Hard

Given the angles α = 45°, β = 30°, γ = 60° and a distance p = 10, express the plane in normal form.

💡 Hint: Convert angles to cosines before substitution into the normal form equation.

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