x y A(6, 6) O OA = 6 6 ( ) OA = 6i + 6j ---- Vektor lajur ---- Vektor i - j 72 6 6 2 2 OA j i 72 6 72 6 Vektor unit arah OA VEKTOR
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x
y
A(6, 6)
O
OA = 6 6
( )OA = 6i + 6j
---- Vektor lajur
---- Vektor i - j
7266 22 OA ji72
6
72
6Vektor unit arah OA
VEKTOR
x
y
B(- 8, 3)
O
OB = - 8 3
( )OB = -8i + 3j
---- Vektor lajur
---- Vektor i - j
733)8( 22 OB ji73
3
73
8
Vektor unit arah OB
VEKTOR
x
y
C(- 7, - 5)
O
OC = - 7 - 5
( )OC = - 7i - 5j
---- Vektor lajur
---- Vektor i - j
74)5()7( 22 OC ji74
5
74
7
Vektor unit arah OC
VEKTOR
x
y
D(4, - 6)
O
OD = 4 - 6
( )OD = 4i - 6j
---- Vektor lajur
---- Vektor i - j
52)6(4 22 OD ji52
6
52
4 Vektor unit arah OD
x
y
A(6, 6)
B(-8, 3)
O
- 14
- 3
AB = - 14 - 3
( )
AB = - 14i - 3j
AB = OB - OA
AB = - 8 6 3 6
( )- ( )AB = - 14 - 3
( )
VEKTOR
x
y
A(6, 6)
D(4, - 6)
O
- 2
- 12
AD = - 2 - 12
( )
AD = - 2i - 12j
AD = OD - OA
AD = 4 6 - 6 6
( )- ( )AD = - 2 - 12
( )
VEKTOR
x
y
B(-8, 3)
D(4, - 6)
O
DB = - 14 - 3
( )DB = - 14i - 3j
DB = OB - OD
DB = - 8 4 3 - 6
( )- ( )DB = - 12 9
( )
- 12
9
VEKTOR
x
y
N(3, 4)
O
OM = -3 5
( )ON = 3i + 4j
---- Vektor lajur
---- Vektor i - j
M(- 3, 5)
Ungkapkan(a)OM dalam bentuk vektor lajur(b)ON dalam bentuk xi + yj
OP = - 2 3
( )
PQ = OQ - OP
PQ = 13 - 2 8 3
( ) - ( )PQ = 15 5( )
OQ = 13 8
( )Diberi dan
R ialah satu titik pada PQ dengan keadaan
Carikan (a) PQ (b) IORI PQPR5
3
PR = OR - OP
OR = PR + OP
OR = 3/5 PQ + OP
OR = 7 6( )IORI = 8567 22
OR = 9 - 2 3 3
( ) + ( )
x
y
P(5, 3)
O
OQ = -8 4
( )ON = 5i + 3j
Q(- 8, 4)
Ungkapkan(a)OP dalam bentuk (b)OQ dalam bentuk xi + yj
xy( )
Gunakan maklumat di atas untuk menentukan nilai h dan nilai k apabila r = 3p – 2q
p = 2a + 3bq = 4a – br = ha + (h – k )b, dengan keadaan h dan k adalah pemalar
ha + (h – k)b = 3(2a + 3b) – 2(4a – b)
Bandingkan vektor a dan b
a: h = 6 – 8 = - 2
b: h - k = 9 + 2 - 2 – k = 11 - 13 = k
r = 3p – 2q
AB = 5 7
( )
AB = OB - OA
OA = 2 5 3 7
( ) - ( )OA = -3 - 4( )
OB = 2 3
( )Diberi , dan , carikan
(a)koordinat A(b)vektor unit dalam arah OA (c)Nilai k jika CD selari dengan AB
IOAI = 5)4()3( 22
CD = k 5
( )
OA = OB - AB
(a) (b)
ji5
4
5
3
Vektor unit arah OA
Koordinat A ( -3, - 4)
AB = 5 7
( )
CD = m OA
k -3
5 -4
( ) = m ( )
OB = 2 3
( )Diberi , dan , carikan
(a)koordinat A(b)vektor unit dalam arah OA (c)Nilai k jika CD selari dengan AB
CD = k 5
( )
(c)
5 = - 4 m
Bandingkan:
- 5/4 = m k = - 3 mdan
k = - 3 ( - 5/4) k = 15/4
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