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Title: Vectors
Description: Revision questions on vectors for high school students
Description: Revision questions on vectors for high school students
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1
...
Gi
v
ent
hat
and
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i
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a)(
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)
(
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)
(
3mks)
|
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(
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(
b)Showt
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,
B(
3,
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5,
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ecol
l
i
near
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...
Gi
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ent
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(
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er
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net
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(
4mks)
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(
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(
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Gi
v
ent
hepoi
nt
sP(
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3)
,
Q(
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6,
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essPQandQRascol
umnv
ect
or
s
...
4
...
Fi
nd
(
2
mks)
5
...
Theposi
t
i
onv
ect
or
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e 2 and 8 r
espect
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el
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...
(
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ks)
7
...
Fi
ndt
hecol
umnv
ect
or
s;
(
a)
(
b)|
(
1mk)
|
(
2mks)
8
...
...
(
3mks)
10
...
│p+q│
(
1mk)
(
b)│ p–2q│ (
2mks)
11
...
1
Si
n60oSi
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12
...
Fi
ndt
hecoor
di
nat
esoft
hepoi
ntwhi
chdi
v
i
desAB
~ ~
~
~
i
nt
er
nal
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yi
nt
her
at
i
o1:
3
13
...
I
nat
r
i
angl
eOAB,
M andNar
epoi
nt
sonOAandOBr
espect
i
v
el
y
,
sucht
hatOM:
MA=2:
3
andON:
NB=2:
1
...
Gi
v
ent
hatOA=aandOB=b
O
~
~
M
N
B
(
a)Ex
pr
essi
nt
er
msofaandb
~
~
(
i
)BM
A
(
i
i
)AN
(
b)Byt
aki
ngBX=tandAX=hAN,
wher
etandhar
escal
ar
s,
expr
essOXi
nt
wo
di
f
f
er
entway
s
(
c)Fi
ndt
hev
al
uesoft
hescal
ar
standh
(
d)Det
er
mi
net
her
at
i
osi
nwhi
chXdi
v
i
des:
(
i
)BM
(
i
i
)AN
15
...
I
fOi
st
heor
i
gi
nandP
t
hemi
dpoi
ntofAB
...
a)I
fA,
B&Car
et
hepoi
nt
s(
2,
-4)
,
(
4,
0)and(
1,
6)r
espect
i
v
el
y
,
uset
hev
ect
ormet
hod
t
of
i
ndt
hecoor
di
nat
esofpoi
ntDgi
v
ent
hatABCDi
sapar
al
l
el
ogr
am
...
Ri
sanot
herpoi
ntwi
t
h
~
~
posi
t
i
onv
ect
orr=3/
½p
...
(
i
i
i
)Det
er
mi
net
her
at
i
oPQ :QR
17
...
Gi
v
ent
hat
PT:
TM =5:
1,
f
i
ndt
hev
al
ueofk
18
...
I
nat
r
i
angl
eOAB,
M andNar
epoi
nt
sonOAandOBr
espect
i
v
el
y
,
sucht
hatOM:
MA=2:
3and
ON:
NB=2:
1
...
Gi
v
ent
hatO
A=
a
a
n
dO
B=b
~
~
(
a)Ex
pr
essi
nt
er
msof
aandb:
~ ~
(
i
)BM
~
(
i
i
)A
N
~
(
b)Taki
ngBX=kBM andAX=hANwher
ekandhar
econst
ant
sexpr
essOXi
nt
er
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~
~
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,
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,
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n
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nt
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nt
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i
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nt
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...
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t
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nt
er
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21
...
115800t
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er
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nt
o
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ar
st
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oughabankatt
her
at
eof76
...
Thebankchar
gesacommi
ssi
onof2
½%
oft
heamountexchanged
...
Gi
v
ent
hat
:
-r=5i
–2j
andm
2i
+6j
–kar
et
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t
i
onv
ect
or
sf
orRandM r
espect
i
v
el
y
...
OABCi
sat
r
apezi
um i
nwhi
chOA=aandAB=b
...
~ ~
~ ~ ~
Ti
sapoi
ntonOCpr
oducedsot
hatOC:
CT=2:
1
...
Gi
v
ent
hata
–2kand
3i
+4j
–kf
i
nd:
~ =2i+j
~b=|
a+b|
...
I
nt
hef
i
gur
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ow,
Ei
st
hemi
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...
Thecoor
di
nat
esofpoi
ntO,
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BandCar
e(
0,
0)(
3,
4)(
11,
6)and(
8,
2)r
espect
i
v
el
y
...
Apoi
ntQdi
v
i
desABi
nt
her
at
i
o7:
2
...
Fi
ndt
hecoor
di
nat
esofQ
Title: Vectors
Description: Revision questions on vectors for high school students
Description: Revision questions on vectors for high school students