39. CHALLENGE Tell whether each of the following situations involving three planes is possible. If a situation is possible, make a sketch. a. None of the three planes intersect. b. The three planes intersect in one line. c. The three planes intersect in one point. d. Two planes do not intersect. The third plane intersects the other two. e. Exactly two planes intersect. The third plane does not intersect the other two. PROBLEM SOLVING EVERYDAY INTERSECTIONS What kind of geometric intersection does the photograph suggest? 40. 41. (43.) SHORT RESPONSE Explain why a four-legged table may rock from side to side even if the floor is level. Would a three-legged table on the same level floor rock from side to side? Why or why not? @Home Tutor for problem solving help at classzone.com 44. SURVEYING A surveying instrument is placed on a tripod. The tripod has three legs whose lengths can be adjusted. a. When the tripod is sitting on a level surface, are the tips of the legs coplanar? 42. b. Suppose the tripod is used on a sloping surface. The length of each leg is adjusted so that the base of the surveying instrument is level with the horizon. Are the tips of the legs coplanar? Explain. @Home Tutor for problem solving help at classzone.com 1.1 Identify Points, Lines, and Planes 45. MULTI-STEP PROBLEM In a perspective drawing, lines that do not intersect in real life are represented by lines that appear to intersect at a point far away on the horizon. This point is called a vanishing point. The diagram shows a drawing of a house with two vanishing points. a. Trace the black line segments in the drawing. Using lightly dashed lines, join points A and B to the vanishing point W. Join points E and Fto the vanishing point V.
39. CHALLENGE Tell whether each of the following situations involving three planes is possible. If a situation is possible, make a sketch. a. None of the three planes intersect. b. The three planes intersect in one line. c. The three planes intersect in one point. d. Two planes do not intersect. The third plane intersects the other two. e. Exactly two planes intersect. The third plane does not intersect the other two. PROBLEM SOLVING EVERYDAY INTERSECTIONS What kind of geometric intersection does the photograph suggest? 40. 41. (43.) SHORT RESPONSE Explain why a four-legged table may rock from side to side even if the floor is level. Would a three-legged table on the same level floor rock from side to side? Why or why not? @Home Tutor for problem solving help at classzone.com 44. SURVEYING A surveying instrument is placed on a tripod. The tripod has three legs whose lengths can be adjusted. a. When the tripod is sitting on a level surface, are the tips of the legs coplanar? 42. b. Suppose the tripod is used on a sloping surface. The length of each leg is adjusted so that the base of the surveying instrument is level with the horizon. Are the tips of the legs coplanar? Explain. @Home Tutor for problem solving help at classzone.com 1.1 Identify Points, Lines, and Planes 45. MULTI-STEP PROBLEM In a perspective drawing, lines that do not intersect in real life are represented by lines that appear to intersect at a point far away on the horizon. This point is called a vanishing point. The diagram shows a drawing of a house with two vanishing points. a. Trace the black line segments in the drawing. Using lightly dashed lines, join points A and B to the vanishing point W. Join points E and Fto the vanishing point V.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:39. CHALLENGE Tell whether each of the following situations involving
three planes is possible. If a situation is possible, make a sketch.
a. None of the three planes intersect.
b. The three planes intersect in one line.
c. The three planes intersect in one point.
d. Two planes do not intersect. The third plane intersects the other two.
e. Exactly two planes intersect. The third plane does not intersect the
other two.
PROBLEM SOLVING
3
EVERYDAY INTERSECTIONS What kind of geometric intersection does the
photograph suggest?
42
40.
41.
42.
(43.) SHORT RESPONSE Explain why a four-legged table may rock from side
to side even if the floor is level. Would a three-legged table on the same
level floor rock from side to side? Why or why not?
@Home Tutor for problem solving help at classzone.com
44. SURVEYING A surveying instrument is placed on a
tripod. The tripod has three legs whose lengths can
be adjusted.
a. When the tripod is sitting on a level surface, are the
tips of the legs coplanar?
b. Suppose the tripod is used on a sloping surface.
The length of each leg is adjusted so that the base
of the surveying instrument is level with the horizon.
Are the tips of the legs coplanar? Explain.
@Home Tutor for problem solving help at classzone.com
45. MULTI-STEP PROBLEM In a perspective drawing, lines that do not
intersect in real life are represented by lines that appear to intersect at
a point far away on the horizon. This point is called a vanishing point.
The diagram shows a drawing of a house with two vanishing points.
a. Trace the black line segments in the drawing. Using lightly dashed
lines, join points A and B to the vanishing point W. Join points E and
F to the vanishing point V.
1.1 Identify Points, Lines, and Planes
7
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