Exercise 1. Determine the horizontal trace of the plane P which contains the straight line q. 1x21x2...
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Exerci se 1. Determine the horizontal trace of the plane P which contains the straight line q. 1 x 2 q’ q” Q 2 ’ Q 2 ” r 2 Q 1 ” Q 1 ’ r 1
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Transcript of Exercise 1. Determine the horizontal trace of the plane P which contains the straight line q. 1x21x2...
Exercise1. Determine the horizontal trace of the plane P which contains the straight line q.
1x2
q’
q”
Q2’
Q2”
r2
Q1”
Q1’
r1
2. Determine the vertical projection of the line a contained in the plane .
s1
s2
a’A1’
A1’’A2’
A2’’
a’’a) b)
A2’
A2’’ A1’
A1’’
a’’
x
s2
s1
a’
x
c)
s1
s2
a’
x
= a’’d)
s1
s2
x
a’
Remark: if the plane is a horizontal projection plane, then the vertical projection of the line a can not be determined.
a) Determine the vertical projection of the horizontal principle line a of the plane .
s1
s2
a’
a’’
b) Determine the vertical projection of the vertical principle line m of the plane P.
m’
r1
r2
x
m’’
A2’
A2” M1’
M1”
x
3. Determine the vertical projection of the principal line.
4. Determine the vertical projection of the 1st steepest line a in the plane .
s1
s2
a’
a’’
.
A2”
A1’
A2’ A1” x
5. Detremine the traces of the plane for which the line p is the 2nd steepest line of the plane.
s1
s2
.
P1’
P1”P2’
P2” p’’
p’
x
s1
s2
T’’
x
a) By using the 1st steepest line determine the vertical projection of the point T in the plane .
s1
s2
b’’
T’
T’’
b) By using the vertical principle line determine the horizontal projection of the point T in the plane .
m’’
m’T’
b’
.
B1’B2’B1”
B2”
M1’
M1”
x
6. Determine the projection of a point.
Remark: a point in a plane is determined by any line lying in the plane that passes throught the point
7. Determine the horizontal projection of a line segment AB in the given plane .
1x2
s2
s1
A”
B”
p”
P2”
P2’P1”
P1’
p’B’
A’
s”
s’
Contruction of the traces of a plane determined by
a) two intersecting lines
a’’
a’ A1’
A1’’
A2’
A2’’
B2’
b’
b’’
B2’’
B1’’
B1’r1
r2
x
b) two parallel lines
x
m’
m’’
n’
n’’
N1’’
N1’
N2’
N2’’
M1’’
M1’
M2’
M2’’ r2
r1
S”
S’
A plane can determined also with a point and a line that are not incident, and with three non-colinear points. These cases are also solved as these two examples.
q’’
q’
Intersection of two planes
r1
r2
s1
s2
Q1’
Q1’’
Q2’
Q2’’
Q1 r1, Q1 s1 Q1 = r1 s1
Q2 r2, Q2 s2 Q2 = r2 s2
q’’
x
Remark. The horizontal projection of the intersection line coincides with the 1st trace of the plane (horizontal projection plane).
a)
s1 r1
r2
s2
x
b)
Q1’
Q1’’
Q2’
Q2”
q’
1. Determine the traces of the plane which is parallel with the given plane P and contains the point T.
r1
r2
x
T’’
T’
m’’
m’M1’
M1’’
s1
s2
Solved exercises
2. Construct the traces of the plane which contains the point P and is parallel with lines a and b.
x
b’
b’’
a’’
a’
P’’
P’
Remark. A line is parallel with a plane if it is parallel to any line of the plane.
p’
p’’ q’’
q’
r2
r1
P2”
P2’ P1”
P1’
Q1’
Q1”
Instruction: Construct through the point P lines p and q so that p || b and q || a is valid.
m”
m’
n”
n’
m”
m’
3. Construct the traces of the plane determined by a given line and a point not lying on the line
x
4. Construct the traces of the plane determined by the 3 non-colinear given points
p’’
p’
T’
T’’
Instruction. Place a line throught the point T that intersect (or is parallel with) the line p. Here the chosen line is the vertical principle line.
M’
M’’
M1’’
M1’
P2’’
P2’P1’’
P1’
s1
x
A’
A’’
C’’
C’
B’
B’’
r1
r2
r2
M1’
M1”
M2’
M2”
N1’
N1”
N2’
N2”
5. Detremine the 1st angle of inclination of the plane for which the line p is the 2nd steepest line of the plane.
s1
s2
.
To determine the 1st angle of inclination we can use any 1st steepest line t of that plane.
t’
1
P1’
P1”P2’
P2”
T1’
T2’
T20
T2”
p’’
p’
x
6. Determine the intersection of planes P and .
x
z
y
y
r2
r1
s1
s2r3
s3 t’’’t’’
t’
7. Construct the plane throught the point T parallel with the symmetry plane.
s1 s2 k1 k2
z
y
s3
T’
T”T’’’
d3
d1=d2
