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 2 Determine ID: 930745
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Slide1
Exercise
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
Slide22.
Determine the vertical projection of the line a contained in the plane .
s
1
s
2
a’
A
1
’
A
1
’’
A
2
’
A
2
’’
a’’
a)
b)
A
2
’
A
2
’’
A
1
’
A
1
’’
a’’
x
s
2
s
1
a’
x
Slide3c)
s
1
s
2
a’
x
=
a
’’
d)
s
1
s
2
x
a’
Remark
:
if
the
plane
is a horizontal
projection
plane,
then
the
vertical
projection
of
the
line
a
can
not
be
determined
.
Slide4a) Determine
the vertical projection of the horizontal principle line a of the plane .
s
1
s
2
a’
a’’
b)
Determine
the
vertical projection of
the vertical principle line m of the plane P.
m’
r
1
r
2
x
m’’
A
2
’
A
2
”
M
1
’
M
1
”
x
3.
Determine
the
vertical
projection
of
the
principal line
.
Slide54. Determine
the vertical projection of the 1st steepest line a in the plane .
s
1
s
2
a’
a’’
.
A
2
”
A
1
’
A
2
’
A
1
”
x
5.
Detremine
the
traces
of
the
plane
for
which
the
line
p
is
the
2nd
steepest
line
of
the
plane.
s
1
s
2
.
P
1
’
P
1
”
P
2
’
P
2
”
p’’
p’
x
Slide6s
1
s
2
T’’
x
By
using
the 1st steepest line determine the vertical
projection of the point T
in the plane .
s
1
s
2
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’
.
B
1
’
B
2
’
B
1
”
B
2
”
M
1
’
M
1
”
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
Slide77.
Determine the horizontal projection of a line segment AB in the given plane .
1
x2
s
2
s
1
A”
B”
p”
P
2
”
P
2
’
P
1
”
P
1
’
p’
B’
A’
s”
s’
Slide8Contruction of the traces
of a plane determined bya) two intersecting lines
a’’
a’
A
1
’
A
1
’’
A
2
’
A
2
’’
B
2
’
b’
b’’
B
2
’’
B
1
’’
B
1
’
r
1
r
2
x
b)
t
wo
parallel
lines
x
m’
m’’
n’
n’’
N
1
’’
N
1
’
N
2
’
N
2
’’
M
1
’’
M
1
’
M
2
’
M
2
’’
r
2
r
1
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
.
Slide9q’’
q’Intersection
of
two
planes
r
1
r2
s1
s2
Q1’
Q
1’’
Q
2’
Q2’’Q1
r1, Q1 s1
Q1 = r1 s1Q
2
r2, Q2 s2
Q2 = r2 s
2q’’
x
Remark
. The
horizontal
projection
of
the
intersection
line
coincides
with
the
1st
trace
of
the
plane
(
horizontal
projection
plane
).
a)
s
1
r
1
r
2
s
2x
b)
Q
1’
Q
1’’
Q2’
Q
2”
q’
Slide101. Determine
the traces of the plane which is parallel with the given plane P and contains the
point
T.
r
1
r
2
x
T’’
T’
m’’
m’
M
1
’
M
1
’’
s
1
s
2
Solved
exercises
Slide112. 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’
r
2
r
1
P
2
”
P
2
’
P
1
”
P
1
’
Q
1
’
Q
1
”
I
nstruction
:
Construct
through
the
point
P
lines
p
and
q
so
that
p
||
b
and
q
||
a
is
valid
.
Slide12m”
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’’
M
1
’’
M
1
’
P
2
’’
P
2
’
P
1
’’
P
1
’
s
1
x
A’
A’’
C’’
C’
B’
B’’
r
1
r
2
r
2
M
1
’
M
1
”
M
2
’
M
2
”
N
1
’
N
1
”
N
2
’
N
2
”
Slide135.
Detremine the 1st angle of inclination of
the plane
for which the line p is the 2nd steepest line
of the plane.
s
1
s
2
.
To
determine
the 1st angle
of inclination we
can use any 1st steepest line t of that
plane.
t’
1
P
1
’
P
1
”
P
2
’
P
2
”
T
1
’
T
2
’
T
2
0
T
2
”
p’’
p’
x
Slide146. Determine the intersection of planes P
and .xz
y
y
r
2r
1
s
1s2
r
3
s
3
t’’’
t’’
t’
Slide157. Construct the plane throught
the point T parallel with the symmetry plane.s1
s
2 k1 k2
zy
s3
T’
T”
T’’’
d
3
d
1
=d
2