Practice General Form (6.1) - 3D Geometry - IB 10 Mathematics – Group 5, Geometry & Trigonometry

Practice: General Form

Lesson 6.13D Geometry

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9 questions

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3 cards from this section. Quick, good the night before a test.
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6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the general form of the equation for a plane in 3D?
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Think about how 2D lines are expressed, but now incorporate a third dimension.
Question 2.
What do the components A, B, and C represent?
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These ratios tell us about the orientation of the plane.
3Question 3.
What does the general equation of a plane in 3D look like?
- Ax + By + Cz + D = 0
- Ax + By + C + D = 0
- Ax + B + Cz = 0
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It includes three variables and a constant.
4Question 4.
The value of D changes, what aspect of the plane does it affect?
- True
- False
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Think about if the plane moves vertically or not.
Question 5.
Determine the equation of a plane that passes through the point (2, -1, 3) and has a normal vector (4, 5, 6).
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Substituting the point appropriately will help in forming the equation.
Question 6.
Discuss the intersection of two planes given by the equations x + 2y + 3z + 4 = 0 and 2x - y + z - 2 = 0. Analyze their normal vectors to find the angle between them.
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Parallel planes will have a dot product of 1; here, use the angles to measure their intersection.

5 more questions in this section. Enroll free to practise them all.