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A plane surface may be of any shape

e.g. circular or polygon, regular or irregularetc..

PROJECTIONS OF PLANESDefinition of Plane:

A plane surface or figure has only two

dimensions i.e length and breadth and hasno or negligible thickness.

A plane surface may be representedby;(a)Three Points not on a Straight line

(b)Two intersecting lines(c)A line and a point not lying on that line(d)Two parallel lines

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(1) Three Points not on a Straight lineb.

YX

.

c.a

b.

a.

. c

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(2) Two intersecting lines

cd

d

c

X

Y

a

b

b

a

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a

b

X Y

.

p

b

a

p.

(3)A line and a point not lying on that line

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c

d

X Y

a b

d

c

(4) Two parallel lines

a

b

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ORIENTATION OF PLANES IN SPACEOrientation of planes in space may be of anytype as stated below;

Class A: Plane parallel to (or contained by)onereference plane and henceperpendicular to both the other planes;

(a) Plane parallel to (or contained by)P.P. andhence perpendicular to both H.P. & V.P.

(b) Plane parallel to ( or contained by) V.P. andhence perpendicular to both H.P. & P.P.

(c) Plane parallel to (or contained by) H.P. and

hence perpendicular to both V.P. & P.P.

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Class B:Plane perpendicular to one reference

plane and inclined to other two planes;(a) Plane perpendicular to V.P. and inclined to

H.P. by & also inclined to P.P.(b) Plane perpendicular to H.P. and inclined to

V.P. by & also inclined to P.P.(c) Plane perpendicular to P.P. and inclined to

H.P. by & to V.P. by

ORIENTATION OF PLANES IN SPACE

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Class C:Planes inclined to all the reference

planes ( i.e. H.P., V.P. and P.P.);- Plane inclined to H.P. by , inclined to V.P. by and also inclined to P.P- Such planes are also called oblique planes

ORIENTATION OF PLANES IN SPACE

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V.P. P.P.

BD

C

A

b,c

b

a

c

d

a,d

b,c

ba

cd

a,d

a,b

c,d

X Y

Class A(1):Plane parallel to P.P. and hence

perpendicular to both H .P. & V.P.

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X

YYX

B, dA, a

D, d C, c

b

a

d

c

a, d b, c

B

AC

D

X

Y

F.V.

T.V.

Class A(2):Plane parallel to V.P. and hence

perpendicular to both H .P. & P.P.

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d

YX

a

b c

a,b c,d

F.V.

T.V.

C

D

B

A

d

b

ca

Y

X

X

Y

Class A(3):Plane parallel to H .P. and hence

perpendicular to both V.P. & P.P.

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b

Y

X

YX

d c

ba

a, d

b, c

b, c

B

C

a, d

a c

X

Y

= T.V.

F.V.

A

d

D

Class B(1):Plane perpendicular to V.P. and inclined

to H .P. by & also inclined to P.P.

.

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Exercise 01:A regular hexagonal plateABCDEF, 30mm side, is resting

on H.P. on one of thesides/edges with surface of theplate making 45 with H.P. andperpendicular to V.P. Draw theprojections of the plate.

G

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ef

d,e

B,b

D,d

c,f

C,c

a,b

A,a

E,e

d

c

X

Y

C

D

E

F

Data Given:

(1) Hexa. Plate Size = 30mm

(2) = 45

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c

Scale: 1:1

a1,b1YX

b

f

e

d

f1

e1

d1b1

d1

,e1

c1,f1

a,b c,f d,e

a1a

Data Given:

(1) Hexa. Plate Size = 30mm

(2) = 45

30

c

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c

X

Y

a b

cd

a, d

b, c

X Y

Y

X

a

b

d

A B

CD

F.V.

T.V.

Class B (2):Plane perpendicular to H.P. and incl ined

to V.P. by & also inclined to P.P.

.

=

.

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Exercise 02:

A square plate PQRS, edge

25mm size, is in space with oneof its corners on V.P. Surface ofthe plate makes 60 with V.P.

and it is perpendicular to H.P.Draw its projections.

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Data Given:

- Square Plate Size=25mm

- =60

X

Y

s

q

p

r

q,sr

P,p

Q

R

S

X

pq,s

r

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Data Given:

(1) Square Plate Size=25mm

(2) =60

q,s

s1

p

s

q

r p1 r1

q1

p r p1

q1,s1

r1

X Y

P

S

Q

R

Cl B (3) Pl di l t P P d i li d

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Class B (3):Plane perpendicular to P.P. and inclined

to H .P. by & to V.P. by

a

b

d

a

d

c

a,b

X

Y

Z

X

YA

B

D

C

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Exercise 03:

A rectangular plate PQRS 30mm X60mm size, is in space with

shorter edge parallel to H.P. and20mm above it. Plate PQRS isperpendicular to V.P. and inclined

to H.P. by such an angle so thatits plan becomes square. Drawthe projections.

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,b

30

60

a,b c,d

20

a1,b1

c1d1

a1 d1

c1b1

X Y

C

DA

B

,a

,c

,d

30

Data Given:

- Size of rectangle=30mmX60mm

-Distance of plane from H.P.=20mm

(plane is parallel to H.P.)

- Size of Plan=square of

30mm X 30mm

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Exercise 04:

A regular pentagonal plate of30mm sides, has one of its cornerson H.P. The plane of the pentagon

is inclined at 45 to the H.P. Theside of the pentagon, which isopposite to the corner, which is on

H.P. is inclined at 30 to the V.P.Draw the projections of the plate.

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e

a

b

c

d

c,d

b,ea

c1,d1

a1

b1,e1

d1

c1

b1

a1

e1

e2

d2 c2

b2

a2

d2

c2

b2

a2

e2

X Y

Scale = 1:1

Data Given- Size of Pentagonal Plate =30mm

- = 45- = 30

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Exerc ise 05:

Draw the projections of a circle of

75mm diameter resting on theH.P. on a point A of thecircumference. Plane is inclined

to the H.P. such that the plan of itis an ellipse of minor axis 30mm.The plan of the diameter,thorough the point A, is makingan angle of 30 with the V.P.Measure the angle of the planewith the H.P.

Data Given:

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Data Given:

(1) Circle Dia.=75mm

(2) =30(3) Minor axis plan

length=30mm

ab,h

X

75

a

bc

d

e

f

g

h

c1

f1

b2

d2

f2g2

h2 e2

a2

a2h2 b2

c2c1,g1

d2

e2

f2

g2

e1

a1 c,gd,fe

c2

d1,f1

b1,h1

30Scale:1:1

a1

b1 d1

e1

g1h1

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Exercise 06:

A regular hexagonal plate40mm side is resting on one ofits edges on H.P. The planemakes an angle of 30 to H.P.and its longest diagonal makesan angle of 45 with V.P. Drawits projections.

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b

a2

b2 c2

d2

e2f2

f2

e2 d2

c2

b2

a2f1

e1

d1

c1

b1

a1e

d

c

f

deab

a

Xcf c1f1

d1e1

Scale = 1:1

Data given :-(1) Regular hexagonal plate size = 40mm

(2) =30

(3) = = 45

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Exercise 07:

A square plate of side 50mmis held on a corner on H.P.with a diagonal horizontal and

inclined at 40 to V.P. Theplate is seen as a rhombus inplan with one of its diagonals

measuring 40mm. Draw itsprojections and determine theangle it makes with H.P.

D t Gi

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Data Given:(1)Plate =50mm sq.

(2)Plate Diagonal =parallel to H.P. & at 40( ) to V.P.(3)Plate is seen as rhombus with one diagonal=40mm

b2a2

d2 c2

=a2

b2

c2

d2

c1

b1d1a1d1

c1

b1

a1

d

c

b

a

YXa cbd

T.S.

square

40

L

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Exercise 08:

A regular pentagon ABCDE, of25mm sides, has its side AB inthe V.P. and inclined at an

angle of 45 to the H.P. Thecorner A is 20mm above H.P.and the corner D is 25mm infront of V.P. Draw theprojections of the plane andfind its inclination with the V.P.

Data Given:-

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-:Answer:-

= 31

Data Given:-

(1) Regular pentagonal plate size=25mm

(2) =45(3) A= 20 mm above XY line(4) D= 25 mm below XY line

Scale=1:1

20

X

25

a

b

e

d

c

a,b c,e d

e1a1

d1

b1 c1

d2

c2

e2 b2

a2

25

c1,e1

a1,b1

d1

e2

d2

c2

b2

a2

Locus of d

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Exercise 09:

A 30- 60 set square has itsshortest side 40mm long and is inthe H.P. The top view of the set

square is an isosceles triangleand the hypotenuse of the setsquare is inclined at an angle of

45 with the V.P. Draw theprojections of the set square andfind its inclination with the H.P.

D t

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4

0

60

30

a1

b1c1

a1,b1 ca,b

b c

a

4

0

40

c1

b2

c2

a2

a2

b2

c2

Locus of c

X Y

Scale:-1:1

Locus of c

Data:-

(1) T.L.(AB)=40mm

(2) =45

Answer:-(1) = 55

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Exercise 10:

ABCD is a rhombus of diagonalsAC=120mm and BD=60mm. Itscorner A is in the H.P. and thePlane is inclined to the H.P.such that the plan appears to bea square. The plan of diagonalAC makes an angle of 30 to theV.P. Draw the projections ofthe plane and find its inclination

with H.P.

Data:-

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c2

b2a2

d2

a2

d2

c2

b2

c1

30

b1d1

a1d1

c1

b1

a1c

d

a

b

60

b,dYX

a c

120 60Scale:-1:1

Data: (1) Size of rhombus = 120 mm X 60mm

(2) =30Answer:-

(1) =60

E i 11

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Exercise 11:

A regular hexagonal plate 40mm

side is resting on one of itscorners in H.P. The diagonalthrough that corner is inclinedat 30 to H.P. and

(a)the plan of that diagonal is

inclined to V.P. by 30 and

(b)diagonal is inclined at 30.

Draw its projections.

Data Given: -

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b1 c1

d1

e1f1

a1d

e

f

a

b c40

abf

ce d a1

b1f1 c1e1

d1d2 d2

c2

d1

d2

c2

b2

a2

f2

b2f2

e2

c2

d2

e2f2

a2

b2

c2e2

f2a2

Y

b2

e2

Scale=1:1

Locus of d

a2

Data Given: -

(1) Hexagonal plate size=40mm

(2) =30(3) =30 [for case (a)](4) =30 [for case (b)]

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A square plate having size 40

mm, is resting on V.P. with one

of its corner . The plane is

inclined to V.P. by 40. Thediagonal passing through the

point which is on V.P. ,is inclined

at 30 to the H.P. Draw itsprojection.

DATA :

(1) =40

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LOCUS OF C2

d2

C2C3

(2) =30

(3) Size of square =40 mm

Scale :- 1:1

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PROJECTIONS OF

PLANES