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2 days ago · Yes, this figure represents a plane because it contains at least three points, points A A and D D form a line segment, and neither point B B nor point C C is on that line segment. Your Turn 10.5 For the following exercises, refer to the given figure.
- Angles
When two parallel lines are crossed by a straight line or...
- Introduction
This chapter begins with a discussion of the most basic...
- 12.5: Lines and Planes
The equation of a line in two dimensions is \(ax+by=c\); it...
- Angles
Aug 17, 2024 · This may be the simplest way to characterize a plane, but we can use other descriptions as well. For example, given two distinct, intersecting lines, there is exactly one plane containing both lines. A plane is also determined by a line and any point that does not lie on the line.
Dec 21, 2020 · The equation of a line in two dimensions is \(ax+by=c\); it is reasonable to expect that a line in three dimensions is given by \(ax + by +cz = d\); reasonable, but wrong---it turns out that this is the equation of a plane. A plane does not have an obvious "direction'' as does a line.
- Defining Lines. For the following exercises, use this line (Figure 10.4). Figure 10.4. Define DE¯DE¯. Define FF. Define DF↔DF↔. Define EF¯EF¯. Solution.
- Determining the Best Route. View the street map (Figure 10.6) as a series of line segments from point to point. For example, we have vertical line segments AB¯AB¯, BC¯,BC¯, and CD¯CD¯ on the right.
- Identifying Parallel and Perpendicular Lines. Identify the sets of parallel and perpendicular lines in Figure 10.9. Figure 10.9. Solution. Drawing these lines on a grid is the best way to distinguish which pairs of lines are parallel and which are perpendicular.
- Defining Union and Intersection of Sets. Use the line (Figure 10.10) for the following exercises. Draw each answer over the main drawing. Figure 10.10.
A plane does not have an obvious “direction” as does a line. It is possible to associate a plane with a direction in a very useful way, however: there are exactly two directions perpendicular to a plane. Any vector with one of these two directions is called normal to the plane. While there are many normal vectors to a given plane, they are ...
For example, given two distinct, intersecting lines, there is exactly one plane containing both lines. A plane is also determined by a line and any point that does not lie on the line. These characterizations arise naturally from the idea that a plane is determined by three points. Perhaps the most surprising characterization of a plane is ...
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The straight line is parallel to the plane. The straight line is contained within the plane. The straight line intersects the plane. Answer . The figure shows a plane, defined as 𝑋, that extends infinitely in all directions. We observe from the diagram that point 𝐴 lies on plane 𝑋. We also see that point 𝐴 lies on line 𝐿.
