Skew lines

1. Skew Lines
Topic Integration

2. DESIGN AND COMMUNICATION GRAPHICS
Solutions to problems should be taught with….
“an explanation as to how the construction was derived ”
Draft Guidelines for Teachers (page 14)
Two key concepts of plane and descriptive geometry
relating to skew lines are
parallel lines
the parallel plane
Understanding theWhyrather than knowing theHow

3. “Define the concept of skew lines and their use in solving practical problems”
page 17 of syllabus
Clearances between cables, pipes and braces
Shortest connecting tunnel between two mine tunnels
Shortest connection between two oblique sewer lines or pipelines
PROPERTIES AND PROJECTIONS OF SKEW LINES

4. If you look at a bridge over a river, you are looking at an example of skew lines.
Skew lines are lines which are non-intersecting and non-parallel.
Skew lines are
non-coplanar

5. An overpass is an excellent example of skew lines. The roadway represents one
line and the pedestrian bridge represents another line.The “lines” do not intersect
because they are on different planes.

6. C1
D
B
A
C
A1
D1 B1
C1
A
C
D
B
A1
D1
B1
Skew Lines
Skew lines do not intersect. Their
apparent point of intersection will not
align in elevation, plan or any other view.
Intersecting Lines
When two lines intersect, the point of
intersection will align in elevation and
plan, and any other view.
Find the vertical distance between the two skew lines?
Which set of lines is skew?

7. THE CONCEPT OF A PARALLEL PLANE

8. PARALLEL LINES REMAIN PARALLEL IN EVERY VIEW
Lines which are parallel in space will appear parallel in all views

9. Parallel Linese D ra w i n g s C o n tro l

10. PARALLEL LINES REMAIN PARALLEL IN EVERY VIEW
Lines which are parallel in space will appear parallel in all views
except
in the views in which they appear as points
or
where one line is behind the other

11. PARALLEL PLANE
If a line is parallel to any line in a plane, it is parallel to the plane

12. C
B
A
D
B
D
C
A
The projections of two skew lines AB and CD are shown.
(a) Find a plane containing the line CD and parallel to the line AB.
(b) Prove that the plane is parallel to the line.

13. Parallel Plane 1e D ra w i n g s C o n tro l

14. C
B
A
D
BD
C
A
C
D
B
A
M
M
true length (strike)
true length (strike)

15. SHORTEST DISTANCE BETWEEN
TWO SKEW LINES

16. What types of applications of skew lines are around us?

17. A B
C
D
A1
B1
C1
D1
The directions of two parachute jumpers landing are represented by the skew linesAB and CD.
(a) Determine the shortest distancebetween the two skew lines.
(b) Determine the projections of this shortest distance.

18. Shortest Distancee D ra w i n g s C o n tro l

19. A
B
C
D
A1
B1
C1
D1
A2
B2
C2
D2
datum line
A3
B3
C3
D3

20. SHORTEST HORIZONTAL DISTANCE
BETWEEN TWO SKEW LINES

21. A B
C
D
A1
B1
C1
D1
The directions of two javelins are represented by the skew linesAB and CD.
Determine the projections of the shortest horizontal distancebetween the two skew lines.

22. Shortest Horizontale D ra w i n g s C o n tro l

23. A
B
C
D
A1
B1
C1
D1
A2
B2
C2
D2
datum line
A3
B3
C3
D3

24. A
B
C
D
A1
B1
C1
D1
T
H
V
traces of plane
director
Where is the other
plane director?

25. Hyperbolic Paraboloide D ra w i n g s C o n tro l

26. MINING GEOMETRY

27. Earth’s surface
headwall
footwall

28. Skew boreholes
Line on headwall
Line on footwall