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Exercise 1.  Determine Exercise 1.  Determine

Exercise 1. Determine - PowerPoint Presentation

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Exercise 1. Determine - PPT Presentation

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

line plane projection determine plane line determine projection point vertical horizontal parallel determined traces 1st steepest construct lines principle

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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

Slide2

2.

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

Slide3

c)

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

.

Slide4

a) 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

.

Slide5

4. 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

Slide6

s

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

Slide7

7.

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’

Slide8

Contruction 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

.

Slide9

q’’

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’

Slide10

1. 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

Slide11

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’

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

.

Slide12

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’’

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

Slide13

5.

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

Slide14

6. Determine the intersection of planes P

and .xz

y

y

r

2r

1

s

1s2

r

3

s

3

t’’’

t’’

t’

Slide15

7. 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