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8/12/2019 5 Waja 2010 f4 Teachers Copy Lines Planes
1/17
Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 1
Learning Area 11: LINES AND PLANES IN 3 DIMENSIONS Worksheet 1.1
Learning Objective 11.1: Uner!tan an u!e the conce"t o# ang$e bet%een $ine! an "$ane! to
!o$ve "rob$em!.
Learning Outcome &ii' (enti#) hori*onta$ "$ane!+ vertica$ "$ane! an inc$ine "$ane!.
Activity 1:Determine base, horizontal planes, vertical planes and inclined planes.
,o$i -a!e ori*onta$
"$ane
/ertica$
"$ane
(nc$ine
"$ane
1
P, P, P,UT+
PT+
U,
TU
2
A-3 A-3 4
/-+
/3A+
/A-5
/3
6
P, P,+
TU/W
UP/+
T,W+
/W+
UP,T
4
7
P, P,
U/+
TP,W+
TPU+
W,/
TU/W
8
A-3 A-3 /3
/A3
/A-+
/-
Teachers copy
A B
C
V
3
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8/12/2019 5 Waja 2010 f4 Teachers Copy Lines Planes
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8/12/2019 5 Waja 2010 f4 Teachers Copy Lines Planes
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 4
Activity 3 :denti!y and name the normal and orthogonal pro"ection o! a line #V on the plane #$%&
in each o! the !ollowing ob"ects
,o$i Norma$ Orthogona$ Projection
1.
/, ,P
2.
/ P
6.
/ P
7.
/, ,P
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8/12/2019 5 Waja 2010 f4 Teachers Copy Lines Planes
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 5
,o$i Norma$ Orthogona$ Projection
8.
/ P
9.
/ P
.
/O PO
;.
/ P
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 6
Learning Area 11 :LINES AND PLANES IN 3 DIMENSIONS Worksheet 3.1
Learning Objective 11.1: Uner!tan an u!e the conce"t o# ang$e bet%een $ine! an "$ane! to !o$ve
"rob$em!.
Learning Outcome &viii' 3etermine the ang$e bet%een a $ine an a "$ane.
Activity 1 :Determine the angle between a line and a plane.
,o$i Norma$ Orthogona$
Projection
ight4 ang$e triang$e Name the
ang$e
1.
Line P/ an P$ane P,
/ P /P
2.
Line W an P$ane P,
W
W
6.
Line U an P$ane P,
UP P
UP
Teachers copy
P
/
P
U
W
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 7
,o$i Norma$ Orthogona$
Projection
ight4 ang$e triang$e Name the ang$e
7.
Line PT an P$ane P,
T, ,P
TP,
8.
Line PW an P$ane P,
W P
WP
9.
Line U an P$ane P,
UP P
UP
.
Line T< an P$ane J
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page
,o$i Norma$ Orthogona$
Projection
ight4 ang$e triang$e Name the ang$e
>.
Line P< an P$ane J
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8/12/2019 5 Waja 2010 f4 Teachers Copy Lines Planes
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 1%
2. (enti#) the $ine o# inter!ection bet%een the t%o given "$ane!:
i.
&a' P$aneABCDan "$aneBC
i' ommon vertice!: @@@an @@@
ii' Line o# inter!ection: @@@@@@..
&b' P$aneABCDan "$aneAD
i' ommon vertice!: @@@an @@@
ii' Line o# inter!ection: @@@@@@..
&c' P$aneADan "$aneAB
i' ommon vertice!: @@@an @@@
ii' Line o# inter!ection: @@@@@@..
ii.
&a' P$aneABCan "$aneACD
i' ommon vertice!: @@@an @@@
ii' Line o# inter!ection: @@@@@@..
&b' P$aneBCDan "$aneABD
i' ommon vertice!: @@@an @@@
ii' Line o# inter!ection: @@@@@@..
&c' P$aneADCan "$aneABD
i' ommon vertice!: @@@an @@@
ii' Line o# inter!ection: @@@@@@..
iii.
&a' P$ane VABan "$ane ABCD
i' ommon vertice!: @@@an @@@
ii' Line o# inter!ection: @@@@@@..
&b' P$ane VBCan "$aneABCD
i' ommon vertice!: @@@an @@@
ii' Line o# inter!ection: @@@@@@..
&c' P$ane VBDan "$aneABCD
i' ommon vertice!: @@@an @@@
ii' Line o# inter!ection: @@@@@@..
Teachers copy
A
A
B C
D
V
D
AB
C
D
B
# C
#C
A D
AD
A E
AE
A C
AC
# D
#D
A D
AD
A #
A#
# C
#C
# D
#D
C
O
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 11
Learning Area11: LINES AND PLANES IN 3"DIMENSIONS Worksheet 6.1
Learning Objective 11.2: Uner!tan an u!e the conce"t o# ang$e bet%een t%o "$ane! to !o$ve
"rob$em!.
Learning Outcome &ii' 3ra% a $ine on each "$ane %hich i! "er"enicu$ar to the $ine o# inter!ection
o# the t%o "$ane! at a "oint on the $ine o# inter!ection.
Activity 1: Thining &mart
3ra% t%o !traight $ine!+ one on each "$ane! !tate+ %hich are "er"enicu$ar to the $ine o# inter!ection
o# the t%o "$ane! at the "oint given./0o( may wor in pairs i! necessary1
E&a'(le:
The "$ane2&%3%ith the "$ane4532at
"oint3.
&a' The "$ane#42& %ith the "$ane4532
at "oint4.
,tate:
i' Line o# inter!ection: @@@@@..
ii' Line %hich i! "er"enicu$ar to the
$ine o# inter!ection at "oint =:@@@@.@ an @@@@@@
,tate:
i' Line o# inter!ection: @@@@@..
ii' Line %hich i! "er"enicu$ar to the
$ine o# inter!ection at "oint4: @@@@.@ an @@@@@@
3ra% the $ine! a! !tate above: 3ra% the $ine! a! !tate above:
Teachers copy
& %
2 3
4 5
NM
LM RM
4
&
#
23
5
3
%
54
$
2
&
#
& %
2 3
4 5
#
2
4
3
5
&
)N
P) )L
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 12
&b' The "$ane#$%& %ith the "$ane53%$
at "oint%.
&c' The "$ane42%$%ith the "$ane 53%
at "oint $.
,tate:
i' Line o# inter!ection: @@@@@..
ii' Line %hich i! "er"enicu$ar to the
$ine o# inter!ection at "oint%:
@@@@.@ an @@@@@@
,tate:
i' Line o# inter!ection: @@@@@..
ii' Line %hich i! "er"enicu$ar to the
$ine o# inter!ection at "oint $:
@@@@.@ an @@@@@@
3ra% the $ine! a! !tate above: 3ra% the $ine! a! !tate above:
Teachers copy
# $
%&
5
3
5
# $
%&
3
5
$
2 3
%
4
4
*R
SR RM
*R
)* *L
%
$
2 3
5
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 13
Activity 2:Do yo( now how to draw6
3ra% the "air o# $ine! "er"enicu$ar to the $ine o# inter!ection #or each o# the "air! o# "$ane! given
be$o%:
1
.
&a'AD)an')
2
.
&b' CDanAD
6.
&a'#78anABCD.
Teachers copy
D
#
B
A C
D
'
)
C
B
D
A
C
D
A
B
#
A
C
78
C
9
0
:
A
)
'
D
A
B
78
D
C
9
0
:
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8/12/2019 5 Waja 2010 f4 Teachers Copy Lines Planes
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 15
Learning Area11: LINES AND PLANES IN 3"DIMENSIONS Worksheet 7.1
Learning Objective 11.2: Uner!tan an u!e the conce"t o# ang$e bet%een t%o "$ane! to !o$ve
"rob$em!.
Learning Outcome &iv' ,o$ve "rob$em! invo$ving $ine! an "$ane! in 64imen!iona$ !ha"e!.
STEPS TO FOLLO,:
S-e( 1: S.e-/0 -0e 0a(e eeg -o -0e o'a-o g8e9
S-e( 2: a; Ide- -0e le o -ee/-o e-
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 16
$uded E&e/e:
$udedSolu-o:
&a' U!ing P)thagora!5 Theorem+D? 12 cm+'? 18 cm
) ? 22 18; +
< @@@@@..
&b' S-e( 1: S-e( 2:
(enti#) the ang$e bet%een the t%o "$ane!
&)anD')'
@@@@@
S-e( 3: S-e( 4:
,ketch the right ang$e triang$e U!ing Trigonometr) atio to
in &tep +. ca$cu$ate the an!%er.
Teachers copy
cm
The #igure !ho%! a right "ri!m %ith a
uni#orm tra"e*iumDa! it! cro!! !ection.a$cu$ate:
&a' the $ength o#)+
&b' the ang$e bet%een the "$ane!
)anD').
= cm
*> cm
)
)
cm
'
'
D
1 cm
D,
D
tanD ?;
12
? 1.8
D < >=.@+oor >=o*E
D
D,
) 4
* cm
'
E cm
D *+ cm
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Program WAJA Negeri Perak Tahun 2010
FORM 4 MATHEMATICS Module 5 : Page 17
No-e:
1.Letter! $abe$$e in the iagram given are ca$$e vertice!.
The $ine o# inter!ection o# t%o "$ane! i! the $ine joining the common vertice! in the t%o
"$ane!.
2.T%o "$ane! inter!ect at a !traight $ine. The !traight $ine i! ca$$e the $ine o# inter!ection
o# the t%o "$ane!.
6.
7.
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A 2 B
D 3 C Line o# inter!ection i!7:0.
Line! "er"enicu$ar to7:0
are7D an7A, :3 an:2
or 0Can 0B.7 : 0
D 3 C
A 2 B
7 : 0
The ang$e bet%een the
$ine! "er"enicu$ar to the
$ine o# inter!ection o# t%o
"$ane! i! the ang$e
bet%een the t%o "$ane!.
Line!
"er"enicu$ar
to the $ine o#
inter!ection
Line o#
inter!ection
#lane +
#lane *
line ofintersection