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R O J E C T I O N S
O F
R A I G H T L I N
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PROJECTIONS OF STRAIGHT LINES
Definition of Straight line:
A straight line is the shortest distancebetween two points.
-Top views of two end points of a straight
line, when joined, give the top view ofthe straight line.
-Front views of the two end points of a
straight line, when joined, give the frontview of the straight line.
Both the above projections are straight
lines.
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Orientation of Straight LineinSpaceA line in space may be parallel,perpendicular or inclined to either the H..
or !.. or both.
"t may be in one or both the referencelanes.
#ine ends may be in different $uadrants.
osition of %traight #ine in space can be
fi&ed by various combinations of data li'edistance of its end points from referenceplanes, inclinations of the line with thereference planes, distance between end
projectors of the line etc.
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Notatioans used for StraightLineTrue length of the
line(
Denoted by )apital letters. e.g. AB*+ mm,
means thattrue lengthof the line is + mm.
Front View Length(
Denoted by small letters. e.g. a-b-* mm,
means thatFront View Lengthis mm.
Top View Length(
Denoted by small letters. e.g. ab*/ mm,
means thatTop View Lengthis / mm.
Inclination of True Length of Line with H.P.(
"t is denoted by 0. e.g. "nclination of the line
with H.. 1or 2round3 is given as 45 meansthat0 * 45.
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Inclination of Front View Length with XY (
"t is denoted by 6. e.g. "nclination of the Front
!iew of the line with 78 is given as 95 means
that 6 * 95.Inclination of Top View Length with XY (
"t is denoted by :. e.g. "nclination of the Top
!iew of the line with 78 is given as 45 meansthat : * 45.
End Projector i!tance:"t is the distance between two projectorspassing through end points of F.!. ; T.!.measured parallel to 78 line.
Inclination of True Length of Line with V.P.(
"t is denoted by
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Line in Dierent Positions withrespect to H.P. & V.P.
)#A%% A(#ine perpendicular to 1or in3 one
reference plane ; hence parallel to boththe other planes
1+3 #ine perpendicular to ..; 1hence3 parallel
to both H.. ; !..
1>3 #ine perpendicular to !..; 1hence3 parallel
to both H.. ; ..
143 #ine perpendicular to H..; 1hence3 parallel to both !.. ; ..
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Line in Dierent Positions withrespect to H.P. & V.P.
)#A%% B( #ine parallel to 1or in3 one
reference plane ; inclined to other twoplanes
1+3 #ine parallel to 1 or in3 !..; inclined to H.. by .
1>3 #ine parallel to 1 or in3 H..; inclined to !.
by
.
143 #ine parallel to 1 or in3 ..; inclined to H.. by ; !.. by .
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Line in Dierent Positions withrespect to H.P. & V.P.
)#A%% )(#ine inclined to all three reference
planes 1 ?bli@ue lines 3
#ine inclined to H.. by , to !.. by and alsoinclined to profile plane.
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P.P..
H.P.
V.P.
Y
X
B
A
a
b
b
a
ba
z x
Y
Class A(1 !L"#$ %$&%$#'")la& *+ P.P. , -$#$
%a&all$l *+ b+*- *-$ +*-$& %la#$s
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X
Y
a
b
H.P.
V.P.
a
b
Class A(1 ! L"#$ %$&%$#'")la& *+ P.P. , -$#$
%a&all$l *+ b+*- *-$ +*-$& %la#$s
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P.P.
a. b
Y1
.
H.P.
V.P.
a
b
a
bX
Y
Class A(1 ! L"#$ %$&%$#'")la& *+ P.P. , -$#$
%a&all$l *+ b+*- *-$ +*-$& %la#$s
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a b
a b
a b
X Y1
.F.V. L.H.S.V.
T.V.
Y
Class A(1 ! L"#$ %$&%$#'")la& *+ P.P. , -$#$
%a&all$l *+ b+*- *-$ +*-$& %la#$s
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X Y
Profile
Plane
a
/0
b
aT.V.T.L.
F.V.T.L.
20
10
Y1
Y1
50
Data given:-
(1T.L. 3044
(2P+"#* A20 b$l+5 H.P.
/044 B$-"#'
V.P.
(/L"#$ "s %$&%$#'")la&*+ P.P.
(6L"#$ "s 1044 l$7* +7P.P.
Sal$ !8 1!1
Exercise 1!8 A L"#$ AB 3044 l+#9 "s %$&%$#'")la& *+ *-$%&+7"l$ %la#$. T-$ $#' A "s 2044 b$l+5 H.P. /044b$-"#' V.P. , 1044 *+ *-$ l$7* +7 P.P. :&a5 *-$%&+;$*"+#s +7 s*&a"9-* l"#$ AB (".$. F&+#* V"$5 , T+%V"$5.
.
..b
.
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V.P.
H.P.
Y
X
A
B
b
a
a b.
Y
XClass A(2!L"#$ %$&%$#'")la& *+ V.P. , (-$#$
%a&all$l *+ b+*- *-$ +*-$& Pla#$s
(".$. H.P. , P.P.
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a b
X
Y
V.P.
H.P.
a
b
.
Class A(2!L"#$ %$&%$#'")la& *+ V.P. , (-$#$
%a&all$l *+ b+*- *-$ +*-$& Pla#$s
Cl A(2 L" '" l * V P , (-
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V.P.
H.P.
a b
X Ya
b
T.V.
F.V..
Class A(2!L"#$ %$&%$#'")la& *+ V.P. , (-$#$%a&all$l *+ b+*- *-$ +*-$& Pla#$s
E i 2 A L" ABC =0 l " '" l
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.
30 a
b
ab
20
)al (AB AC
Answer :-
8 T-$ &$al a#9l$ b$*5$$# *5+
)#$>)al l$9s BAC123@
Bb Aa
ab
Y
L+)s +7 Sal$ !8 1!1
/
L+)s +7
2
/
T.L.
T.L.
T.L.
Exercise 11 :- T5+ a#9+$s +# a *&$$ %la#*$' #$a& *-$
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0.34
14
1.234
0.34>2
F.V.
T.V.
>
>
%
%
Y
L
9 %+4%+)#' 5all +7 a b)#9l+5 a&$ 14 a#' 1.234 ab+$ *-$
9&+)#' a#' 0.34 , 0.34 7&+4 a 134 *-" +4%+)#' 5all
b)* +# *-$ +%%+s"*$ s"'$s +7 "*. T-$ '"s*a#$ b$*5$$# a#9+$s
4$as)&$' al+#9 *-$ 9&+)#' a#' %a&all$l *+ *-$ 5all "s 14.:$*$&4"#$ *-$ &$al '"s*a#$ b$*5$$# $#*&$s +7 *5+ 4a#9+$s.
Data Given :-(1 E.P.:. 14
Answer :-8 *-$ &$al '"s*a#$ b$*5$$#
$#*&$s +7 *5+ 4a#9+$s %>2 1.
Sal$ !8 1!20
(2 P+"#* P 14 ab+$ 9&+)#0.3 b$-"#' 5all
(/ P+"#* 1.234 ab+$ 9&+)#
0.34 "# 7&+#* +7
5all
134
(6 all *-"#$ss 134
L+)s +7 >
>2
Exercise 12 : T-$ F.V. +7 a l"#$ N 0 44 l+#9 4$as)&$s
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Exercise 12 :T-$ F.V. +7 a l"#$ N 0 44 l+#9 4$as)&$s
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TRACS O! A L"N
efinition:hen a line is inclined to a plane, it
will meet that plane, produced ifnecessary. The point where the line orline produced meets the plane is calledtrace.
Hori"ontal Trace: The point of intersection ofthe inclined line with the H.. is calledHori"ontal Traceor simplyH.T.
Vertical Trace:The point of intersection of theinclined line with the !.. is calledVertical Traceor simplyV.T.
Exa4%l$ *+ "ll)s*&a*$
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V.P.
V.P.
H.P..
.
ab
b
a
B
A
Y
X
Exa4%l$ *+ "ll)s*&a*$
*-$ +#$%* +7 *&a$s
F.V.
T.V.
H.T.
-
V.T.
"#PORTANT PO"NTS R$ARD"N$
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"#PORTANT PO"NTS R$ARD"N$TRACS O! A L"N
"f a line is inclined to both H.. ; !.. thenits Front view, h- and !.T. must be on thesame straight line.
e.g. if front view of a line AB is a#$#, then
h,a-,b- and !.T. must be on a same straightline.
"f a line is inclined to both H.. ; !.. thenits Top view, v and H.T. must be on the samestraight line.
e.g. if Top !iew of a line AB is a$, then v, a, b
and H.T. must be on a same straight line.
IPORTANT POINTS REGAR:ING
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IPORTANT POINTS REGAR:ING
TRACES OF A LINE
(1 I7 a l"#$ "s %a&all$l *+ a#? +7 *-$ %la#$ "* -as #+*&a$ )%+# *-a* %la#$.
$.9. I7 *-$ l"#$ "s %a&all$l *+
-+&"z+#*al %la#$ *-$#*-a* l"#$ 5"ll #+* 4$$*
H.P a#' -$#$ *-$&$
5"ll b$ #+ H.T. a#'
+#l? V.T.
A
B
b
a
a b.
V.T.
Y
IPORTANT POINTS REGAR:ING
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IPORTANT POINTS REGAR:ING
TRACES OF A LINE
(1 I7 a l"#$ "s %a&all$l *+ a#? +7 *-$ %la#$ "* -as #+*&a$ )%+# *-a* %la#$.
$.9. I7 *-$ l"#$ "s %a&all$l *+
-+&"z+#*al %la#$ *-$#*-a* l"#$ 5"ll #+* 4$$*
H.P a#' -$#$ *-$&$
5"ll b$ #+ H.T. a#'
+#l? V.T.
V.T.
A Ba
a b
b
D
.
IPORTANT POINTS REGAR:ING
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IPORTANT POINTS REGAR:ING
TRACES OF A LINE
$.9. I7 *-$ l"#$ "s %a&all$l *+
V$&*"al Pla#$ *-$#
*-a* l"#$ 5"ll #+* 4$$*V.P a#' -$#$ *-$&$
5"ll b$ #+ V.T. a#' +#l?
H.T.
Y
X H.P.ab.
V.P.
A
B
a
b
H.T.
IPORTANT POINTS REGAR:ING
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IPORTANT POINTS REGAR:ING
TRACES OF A LINE
$.9. I7 *-$ l"#$ "s %a&all$l *+ V$&*"al Pla#$*-$# *-a* l"#$ 5"ll #+* 4$$* V.P a#' -$#$
*-$&$ 5"ll b$ #+ V.T. a#' +#l? H.T.
20
/0@
b
a
ba
F.V.1T
.L.
T.V.
-
H.T.
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Exercise 13 :A line AB 80 !! l"ng is seen as
a straig#t line "$ lengt# 55!! in its $r"nt
view an% "$ lengt# 65 !! in its t"& view'
(ts en% A is 10 !! a)"ve *'+' , is in $irst.a%rant w#ere as en% B is 25 !! )e#in%
/'+' an% is in ec"n% .a%rant' Draw its
&r"ecti"ns an% $in% ".t its inclinati"nswit# *'+' , /'+' an% als" l"cate its traces'
Data Given:
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1 ''80 !! 2 '/' 55!! 3 '/' 65!!
4 En% A10 !! a)"ve *'+'
('' /'+'
5 En% B a)"ve *'+'
25!! )e#in% /'+'
X Y
b
b
L+)s +7 b
L+)s +7 b
b1
23
b1
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Exercise 14 : #e en% &r"ect"rs %istance "$ a
line er"' (ts en% < is 25!! )el"w*'+' , 40!! )e#in% /'+' w#ere as en% = is
10 a)"ve *'+' , 55!! in $r"nt "$ /'+'
Draw its &r"ecti"ns an% $in% ".t itsinclinati"ns wit# *'+' , /'+' an% als"
l"cate its traces'
Data Given:
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.
10
60
23
4
.
.
.
.
.
Y
4
#
#
#
4
V.T. H.T.
-33
. .
1 En%
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%
-a"#9 *5+ $>)al a&4s AB , BC -"#9$' a* B "s $%*
"# H.P. +# "*s #$$'l$ %+"#* A , C 5"*- *-$ l"#$ ;+"#"#9
A , C "s %$&%$#'")la& *+ V.P. I* "s s$$# "# 7&+#* "$5as a s*&a"9-* l"#$ 10044 l+#9 "#l"#$' a* /0K *+ H.P.
5-"l$ "* "s s$$# "# *+% "$5 as a# a#9l$ a)c wit# @a)c
60K. :&a5 "*s 7&+#* "$5 a#' *+% "$5 a#' 7"#'Q
(1 T-$ -$"9-* +7 %+"#* B ab+$ H.P.
(2 T-$ a%a&* '"s*a#$ b$*5$$# *-$ #$$'l$ %+"#*s
A , C
(/T-$ l$#9*-s +7 a&4s AB , BC 5"*- &$al
b$*5$$# *-$4
Data Given: "c.s "$ )
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Data Given:
1 '/'100 !!f
2
30;3 @a)c 2 60;
4 ac is &er&en%ic.lar
t" /'+' aA
a
C
b1
b1B
b
X Y
HF.V.
60;
"c.s "$ )
"c.s "$ )
b2AB'
"s*.
Answers:
1 AB 112!!
2 2 53;
3 A 100 !!
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Exercise 16 :#e en% A "$ a straig#t line AB
120!! l"ng is 50 !! )e#in% /'+' , 35 !!
)el"w *'+' #e line is incline% t" *'+' )C 30; ,#as a &"int "n it in )"t# t#e re$erence
&lanes' Draw t#e &r"ecti"ns "$ t#e line an%
$in% ".t its inclinati"ns wit# /'+' Als" l"cate itstraces'
Data Given:
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2 ''120 !!3
30;
1 En% A35 )el"w *'+'
50 )e#in% /'+'
4 "n AB in
)"t# re$' +lanes
Answers:
1 45;
2 *'' in/'+', *'+'
3 /'' in /'+'
, *'+'
/3
a
a
b
b
C
1
30
b2
X 1
b1
b1
b2.
.
L+)s +7 b
L+)s +7 b
F.V. +7 AC
T.V. +7 AC
H.T. , V.T..
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PRO%CT"ONS O!STRA"$HT L"NS