Table Of ContentSkills in
Mathematics for
JEE MAIN & Y | ]
PND\VPNN( OTD)
3D Geometry
“With Sessionwise Theory & Exercises
‘Amit M. Agarwal arihant
Skills in
Mathematics for s 7
JEE MAIN & yy.
ADVANCED
Vector &
3D Geometry
With Sessionwise Theory & Exercises
Amit M. Agarwal
>Karihant
ARIHANT PRAKASHAN (Series), MEERUT
Skills in Mathematics for
JEE MAIN & ADVANCED
PREFACE
“FOU CAN DO ANYTHING 1 YOUSET YOUR MIND TO I, TEACH GEOMETRY
‘TO JEE ASPIRANTS BUT BELIEVE THE MOST IMPORTANT FORMULA IS
(COURAGE + DREAMS = SUCCESS”
Isa mater of peat prides honour forme the rected such an overhelning
respons tothe previ ions ofthis book fom th readers Ina wats sind
Inet reise th bok through as per the changed pater of EE Mata & Adeance.
ved make te contents mare relevant per the ees fsdets man ops
oven rewriten, lt fe problems fnew peshevebeen aed inet A
oul efor ae made to remove alte ring eres hat ad celine
‘ions The bok snow in sch hp tht the aes wolfe texte whe ing
"trough the protems whch wl int death concep ton
‘A Sommary of changes that ave been made in Revised & Enlarged Eton
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1+ Themotimprant pot hot ie ian abe ole mateo
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‘ender wilbe ae top tough he lhpterin pena
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Theses comple vndrandng lth oem olJEE quis eee
‘ey ouetans eer kd EE
+ Along ith exe per ith ich sein, compe cate caer hae
enathe endo xh pert ieee compet patie or TE long
‘te asesment of owe they hae ped wi stay fhe hate
Ls 10 Year quis sed in EE Main Ad TIE AEE hve ben cone all
echt
However have mde the bet forts and pt my alteaching experience revising this
tek il am lokng forward to ge thealabe sugpesins nd criticism rom my
‘vm frterity Lethe eternity of EE teacher
{rod like to motivate the sudensto end the suggestions the changes that
they wast tobe incorporated inthis bok Allhe suggestions given y You allie
ptm prime fcu othe tine of nex revise of he book.
AmitM. Agarwal
Skills in Mathematics for
JEE MAIN & ADVANCED
CONTENTS
VECTOR ALGEBRA
LEARNING PART
Send Vor Quatiee
1 Repentaion eee
Postion Vcr of atin pce
cana Reon Vr
naDendDSptene
PAtin & Sean Vectoe
1 Mipeatono Very Sale
PRODUCT OF VECTORS
LEARNING PART
rode To Vests
1-62
+ Secon Forma
Seal
+ Linear Combiotion of Vcore
1 There on Cola
63-166
+ Areot Para and Tange
+ Manentef Fore and Cui
1 Ratton About on Ai
Compose Vesor Mong end Seen
Ferpedcirt Anaer Veter 5 Sear gle dt
+ Aplatn Det Prod ini
Neha
; + ec Tile Prt
+ Vector oe Ca rc Teo
TBE Type eae:
+ Chater Eee
‘Skills in Mathematics for
JEE MAIN & ADVANCED
3. THREE DIMENSIONAL
COORDINATE SYSTEM 167-282
Poston Vcor fe Plt in Spe
1 Siting of Orin
Dita orale
Section Fora Distance fs Pt rom Pane
1 Diecton Cosmet Dicion + ‘Egon lanes Bec te
RasootsYeror ‘Ange bere To Pane
+ Petn ofthe inSegment + Lian Pane
Kinng Two Fantions en Une Sento
Sesion? + Sphere
guton fs Sth Linea Space PRACTICE PART
Ange ewe Two Line panel
1 RependcrDiuneofatoit > Gap tnenion
‘Skills in Mathematics for
JEE MAIN & ADVANCED
SYLLABUS FOR JEE MAIN
‘ThreeDimensional Geometry
Coase as pint in pce, dance between wo points, ection formu
ection ratios and rection cosines anglebetween wo ntersecting ines Skew
lines.the shore distance between them ands equaton. Equations ofaline nd
phneindifeet ors ntersctionofalineanda plane, coplanar lines
Vector Algebra
‘Vectors and lars, adtion of vector, components of 2 vector In two
dimensions and the mensional pce clr and ecto prot, salar and
vectortpleprodect
SYLLABUS FOR JEE ADVANCED
‘Locus Problems
Three Dimensons Direction cosine nd ditcton ration, equation ofa
stright linen pace equation of lane. ditanc ofa pi fom» plane
Vectors
[Adion of vector xa mulation clr products, dot and ross
‘rodut saree rodct and ther geometric ineprtatons
CHAPTER
01
Vector Algebra
Learning Part
Session
+ Soar an cor Quattes
+ Regresttaton of Vectors
Poston vetr of Paitin Space
Direction Coins
1 eanglr Resa of econ 20a 30 Syste
session?
1 Adal & Sobran of Vets
1 nuttin of etry Saar
+ secon Formula
sassion3
= neat Combination of Vectors
{theorem on Copan oe-coplanr Veco
1 near Independence and Dependence of Vectars
Practice Part
+ see Type amples
+ chapter oxreses
"ihant on Your Mobile!
arcs wth he symbol con be prota on your mobile See inside cove page totter
Session 1
‘Scalar and Vector Quanti
s, Representation of Vectors,
Position Vector of a Point in Space, Direction Cosines,
Rectangular Resolution of a Vector in 2D and 3D Systems
Vectors repent on th ot import athena
‘yiems whch swede andl cern psalms
[SGeumetry. Methane and ta trance Ape
Mathematics Phys and ngeing
Scalar and Vector Quantities
est wor temperate ce
‘Asal quantty repented by el ume slong
‘th tei Scrd Kind unseen
‘ch ve bth meg diem ck unter
Secale vectors Duper. vey ecto
‘omentum weight ree ae amis of er
example 1. lasty te flowing eases as
esas and etre
1) 20 mrortwet 6) 10 Newton
(9 30kmy
(So omar oth
(010 eaound
4 Decl dite eee
(i pnts
(ay Yor
(nate pe Se
Representation of Vectors
Oromia et ees by dete ine
Foreaumplja= AB Here. scaled he itil pott nd
‘isch ermal pot or ip
fanatic wien ror above ory oral
tence ashen
arin the ge a= AB and magne of moda of
spends
th The ego AB wb etd by AB) or AB
Seppe! Tein of unmet eng wich AB ise
Segment caled hsppr of he ete AB
Seve The sense of AB sam Ato F and hat o BA
ffm Bio A Tas, the sense ote le seme
rom nal point the ead po.
example 2. sopesent graphical
1 A dpacament fo 80 et of ath
(0 paceman 50 im sutvest,
S61 () The et OF represent the reqied vet.
(Te eer OQ te heed vee
‘Types of Vectors
1. Zero or ml vector A vcore magne 0
‘eal aero or allcor and mest by
“he inland termina pols of the deed ine
Segal repeating sf tr re conde td
1. alt vector A vector whowe moda wy.
‘aed ut vector The wit vector be dein of
Seco a dented by Arad “ep Ths,
6 Coplanar vectors Assen of eters io be
‘ola ty be nt sae le ht
‘Sport re praelto these ne
1. Coterminows vectors Vectors hing te mie
{ermal pnts ee nerminos vector
1. Negative fa yectr Tor vector which asthe same
Toupee piven vectra bt pote
‘econ sealed the eatin ofan is ete
ia Too, 1PQ= a thea QP=— =
4: Reciprocal of a vctr A vector ving he same
(eto tht svn veer ut mage
1 Free vestrs Ith wala ect depends nto
[tapi and incl sondage of
oun nthe pce cad ie vecor
Remark
(chap OF Vector Agata 3
12. Equality of vectors Two vectrsa nd bare sito
teeral
‘@al=161
(they hve the ame or paral upp.
(Gi ey have te ame sense
"Toni vector may ot be egal they have
eve direcon
{example 5. nthe fling ge, which ofthe
1) coer
(eal
(i cost
(9) Cliar bt eu
(0 nea oqo
(0) aint dare colnrar bt hey oe ot eu a ht
Position Vector of
a Point in Space
Leto the id pita spc andX°0X. YOY an
Zz etic ine perpen ech other a0.
‘Ten hese ie ine aed Vain Yanan 2s
sich cone the rectangular cordate yen The
fleses NOY, 102 and ZON ened epee the
plane te 2 pine and the pane
4 Tentook of veer & 30 Geomety
Now, le Peay pnt nace Then postion o Pie
(Brey tad) whee pensar
Sn mn 2 Fane
‘The vector OF ale he pon vector f iat?
wah respect othe origin and writen
sie
where jad ere uit vector pra Xan Yai
sd Zack We uly dente postion etry
Remarks
Ss irelatberaeamerecs reared
relay Wawa
sabe akonbeals af ahamster
Unt vecorpaaid tn sia a
vale of
example 6. wnt no ects gant
ign
sok etn =2h Jo and beds 2h
Den lalatble oP ae
[example 7. ope sie of square be represetd by
the vectors 3i+4) +5 then th area of the squares
wn oo
os on
sy teta sl rasan
Fee = OBS
‘hte enghota eto =
inn rear 253238
Direction Cosines
Let be the potion vcr of pot Fs3.2) Then
renner te cone of npc. BandY
tert vcr nae with he pve deco fF
Salzer rnp We oul denote deci
Ste by itd reece.
Inthe gi we may ote tht SOAP ih angled
ange toda te ave
cova sandfoled
iy. tight angle pes Oa OCP,
wee
cote? and ory!
“has weave the towing
Here 2POX,9= £POY.y= £702 andi) and are
the ut vet long OX, OF ad 2 epctively.
