Practice Equation Of A Plane (8) - Three Dimensional Geometry

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10 questions

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4 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Write the general form of a plane equation with A=1, B=2, C=3, and D=4.
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Substitute the values into the general form Ax + By + Cz + D = 0.
Question 2.
What does the normal vector represent in the equation of a plane?
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Think about the definition of a normal vector.
3Question 3.
What is the general form of the equation of a plane?
- Ax + By + Cz + D = 0
- x + y + z + 1 = 0
- A + B + C + D = 0
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Recall the standard representation for plane equations.
4Question 4.
True or False: The normal vector of a plane can be any vector that lies in the plane.
- True
- False
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Think about the definition of normality in geometry.
Question 5.
A plane passes through the point (1, 2, 3) and has a normal vector n = (4, -5, 6). Write the equation of the plane in general form.
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Use the point-normal form to derive the equation.
Question 6.
Find the angle between the normal vector (1, 0, 1) and the z-axis.
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Consider the direction cosines relating to angles between vectors.

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