Practice General Form (8.1) - Three Dimensional Geometry

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9 questions

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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 of a plane?
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Think about how we express 2D equations but in 3D.
Question 2.
Identify what A, B, and C represent in the general form.
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Remember the role of the normal vector in defining a plane.
3Question 3.
What is the general form of the equation of a plane?
- A x + B y + C z + D = 0
- Ax + By = 0
- x^2 + y^2 + z^2 = 0
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Look at how we express equations of different dimensions.
4Question 4.
True or False: The normal vector is parallel to the plane.
- True
- False
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Think about how 'normal' relates to 'perpendicular'.
Question 5.
Find the equation of the plane that intersects the point (2, 3, 4) and has a normal vector (1, 1, 1). Derive it in all forms.
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Explore how each form derives from the normal vector and the coordinates provided.
Question 6.
Given the plane 2x - y + 3z + 5 = 0 and another plane x + 2y - z - 7 = 0, find the angle between them.
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The angle between planes can be derived from the angle between their normals.

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