Motion. in a plane
Scalan quantity:
A physicat
quanlity that has only
nls magnitd
diection is called
an
doesn'A Neyuie any
ScalaS quantity
Eime, tempaatune ,enemqy etc. ,
ex: Distance,
Vectos uanlity
ohich has both mogpi tude
A physical quontity also cbeu the la oRf
and
an
diaection obey
vectos uantity
Called
vectoa addition
cement , velocity fonce,etc.
ex: displo nepnesented as
xA vecto having moqnitude A
A is
A. A
* Giaphical nepsese ntation tail head or j"
tip
Equality of ec toss:
vectoms A and B said to be equal
Tuoo
have Same magnitude and
if and only if they
Same diaection.
* Multiplying vectoa A usIth positive numbe
bave the ne sultant vecto as
)
then
sith chonge in magoitude but no chonge
in diaection.
,*Multiplying a vec to A oith neqative
umbe
the esullant vectos is, -dA,oith chone
in magnitude and also in diecton.
Taiangle Lo f vecto acdition:
Statemeot:
Any too vectoas
aepnesented by any
too sides of a taicangle token in odea then
the thid side token onden gives
the nesultant vecto.
Consicdea tDo vectOmS A and B tobich
Nepa sente by the
and Pa taken
too sides of
taiangle
io 0de,then
Iepsesents the MeSultant ve cto as R.
R=A t B
Paopeties vecto
yCommu lotive lau addition:
Vectos addition obey
fo too
commulotive low.
vectons
given A ond B
bave
AtB =B+A
i) Asso ciatve Qo
Vecto oddition
cbeys os5ociative
fom qven thaee vectos A,B law.
hove and
CÃ+8) + -
, Null ectog 9 zego vectOn
vec t o ohose .manpitude and dimection
A
c a n n o t
be specified is called null vec to oa
vectoa.
Z e n O
Nepresente by O,
Paallelogmam law of vectoms:
statement
sepNesented by any
IF any t o vectos ae
cf
of oa pasalleloqmam then the
odjace nt sides
too polnt qives
passing thsough the
Same
diagonal too vectons.
the nesultant of th
aepeesented
Let A and BB be any too vectoms
be anu
the
by the odjacent side
shown io fioue.The diagoa
pasallelogiam esultont vectom, R.
nepnesents the
S
fom the tia
taiangle OSN
(os) -(oN÷ + (sN)
(SN
Cos) =(oe+ PN) +
(os - (op+(PN+ 2xoP xPN+ SN
=A+ (PN+ 2xAxPN SN)
fom sNP
COSe = PN
Scalan quantity:
A physicat
quanlity that has only
nls magnitd
diection is called
an
doesn'A Neyuie any
ScalaS quantity
Eime, tempaatune ,enemqy etc. ,
ex: Distance,
Vectos uanlity
ohich has both mogpi tude
A physical quontity also cbeu the la oRf
and
an
diaection obey
vectos uantity
Called
vectoa addition
cement , velocity fonce,etc.
ex: displo nepnesented as
xA vecto having moqnitude A
A is
A. A
* Giaphical nepsese ntation tail head or j"
tip
Equality of ec toss:
vectoms A and B said to be equal
Tuoo
have Same magnitude and
if and only if they
Same diaection.
* Multiplying vectoa A usIth positive numbe
bave the ne sultant vecto as
)
then
sith chonge in magoitude but no chonge
in diaection.
,*Multiplying a vec to A oith neqative
umbe
the esullant vectos is, -dA,oith chone
in magnitude and also in diecton.
Taiangle Lo f vecto acdition:
Statemeot:
Any too vectoas
aepnesented by any
too sides of a taicangle token in odea then
the thid side token onden gives
the nesultant vecto.
Consicdea tDo vectOmS A and B tobich
Nepa sente by the
and Pa taken
too sides of
taiangle
io 0de,then
Iepsesents the MeSultant ve cto as R.
R=A t B
Paopeties vecto
yCommu lotive lau addition:
Vectos addition obey
fo too
commulotive low.
vectons
given A ond B
bave
AtB =B+A
i) Asso ciatve Qo
Vecto oddition
cbeys os5ociative
fom qven thaee vectos A,B law.
hove and
CÃ+8) + -
, Null ectog 9 zego vectOn
vec t o ohose .manpitude and dimection
A
c a n n o t
be specified is called null vec to oa
vectoa.
Z e n O
Nepresente by O,
Paallelogmam law of vectoms:
statement
sepNesented by any
IF any t o vectos ae
cf
of oa pasalleloqmam then the
odjace nt sides
too polnt qives
passing thsough the
Same
diagonal too vectons.
the nesultant of th
aepeesented
Let A and BB be any too vectoms
be anu
the
by the odjacent side
shown io fioue.The diagoa
pasallelogiam esultont vectom, R.
nepnesents the
S
fom the tia
taiangle OSN
(os) -(oN÷ + (sN)
(SN
Cos) =(oe+ PN) +
(os - (op+(PN+ 2xoP xPN+ SN
=A+ (PN+ 2xAxPN SN)
fom sNP
COSe = PN
