This document discusses the projection of planes in three dimensions. It defines a plane as a two-dimensional surface that can be defined by three non-collinear points, two intersecting lines, a line and a point not on the line, or two parallel lines. Planes can be positioned parallel to one reference plane and perpendicular to the other two, perpendicular to one reference plane and inclined to the other two, or inclined to all three reference planes. Examples of each type of plane positioning are shown along with solutions to three exercises involving drawing the projections of different shaped planes.

1. GANDHINAGAR INSTITUTE
OF TECHNOLOGY
Active Learning Assignment
Subject : EG(2110013)
Topic: Projection Of Plane
Name : Vishvesh Jasani (16020107042)
Branch: Computer
Batch : A3
Guided by – Prof. Dhaval Panchal

2. A plane surface may be of any shape
e.g. circular or polygon, regular or irregular
etc..
PROJECTIONS OF PLANES
Definition of Plane:
A plane surface or figure has only two
dimensions i.e length and breadth and has
no or negligible thickness.
A plane surface may be represented
by;
(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

3. POSITIONSOF PLANES IN SPACE
Positions of planes in space may be of any type
as stated below;
Class A: Plane parallel to (or contained by) one
reference plane and hence
perpendicular to both the other planes;
(a) Plane parallel to (or contained by)P.P. and
hence perpendicular to both H.P. & V.P.
(b) Plane parallel to ( or contained by) V.P. and
hence 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.

4. 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 Ө & 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 Ө & to V.P. by 
POSITIONSOF PLANES IN SPACE

5. Class C:Planes inclined to all the reference
planes ( i.e. H.P., V.P. and P.P.);
- Plane inclined to H.P. by Ө , inclined to V.P.
by  and also inclined to P.P
- Such planes are also called oblique planes
POSITIONSOF PLANES IN SPACE

6. H.P.
V.P. P.P.
BD
C
A
b,c
b”
a”
c”
d”
a,d
b,c
b”a”
c”d”
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.

7. X
Y
YX
B, b’A, a’
D, d’ C, c’
b’
a’
d’
c’
a, d b, c
B
A
C
D
X
Y
F.V.
T.V.
Class A(2): Plane parallel to V.P. and hence
perpendicular to both H.P. & P.P.

8. 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.

9. b
Y
X
YX
d c
ba
a’, d’
b’, c’
b’, c’
B
C
a’, d’
a c
X
Y


Ө
Ө = T.V.
F.V.
A
d
D
Class B(1): Plane perpendicular to V.P. and inclined
to H.P. by Ө & also inclined to P.P.
.

10. Exercise 01
A regular hexagonal plate
ABCDEF, 30mm side, is resting
on H.P. on one of the
sides/edges with surface of the
plate making 450 with H.P. and
perpendicular to V.P. Draw the
projections of the plate.

11. ef
d’,e’
B,b
D,d
c’,f’
C,c
a’,b’
A,a
E,e
Ө
d
c
X
Y
C
D
E
F
Data Given:
(1) Hexa. Plate Size = 30mm
(2)  = 450

12. c
Scale: 1:1
a1’,b1’
YX
Ө
b
f
e
d
f1
e1
d1
b1
d1’,e1’
c1’,f1’
a’,b’ c’,f’ d’,e’
a1a
Data Given:
(1) Hexa. Plate Size = 30mm
(2)  = 450
30
c

13. c’
X
Y
a’ b’
c’d’
a, d
b, c
β
X Y
Y
X
a’
b’
d’
A B
CD
F.V.
T.V.
Class B (2): Plane perpendicular to H.P. and inclined
to V.P. by Φ & also inclined to P.P.
.
β = 
.

14. Exercise 02
A square plate PQRS, edge 25mm
size, is in space with one of its
corners on V.P. Surface of the
plate makes 600 with V.P. and it is
perpendicular to H.P. Draw its
projections.

15. Data Given:
- Square Plate Size=25mm
- Φ=600
X
Y
s’
q’
p
r’
q,s
r
P,p’
Q
R
S
X
Φ
p
q,s
r

16. Data Given:
(1) Square Plate Size=25mm
(2) Φ=600
q,s
s1’
p’
s’
q’
r’ p1’ r1’
q1’
p r p1
q1,s1
r1

X Y
P
S
Q
R

17. Class B (3): Plane perpendicular to P.P. and inclined
to H.P. by  & to V.P. by Φ
a’
b’
d’
a
d
c
a”,b”




X
Y
Z
X
YA
B
D
C

18. Exercise 03
A rectangular plate ABCD 30mm X
60mm size, is in space with
shorter edge parallel to H.P. and
20mm above it. Plate ABCD is
perpendicular to V.P. and inclined
to H.P. by such an angle so that
its plan becomes square. Draw
the projections.

19. ,b
30
60
a’,b’ c’,d’
20
a1’,b1’
Ө
c1’d1’
a1 d1
c1
b1
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
Scale- 1:1

20. PROJECTIONS OF
PLANES