Arihant Vector and 3D Geometry Skills in Mathematics for IIT JEE Main Advanced with Sessionwise Theory Exercises Amit M Agarwal PDF
Preview Arihant Vector and 3D Geometry Skills in Mathematics for IIT JEE Main Advanced with Sessionwise Theory Exercises Amit M Agarwal
Skills 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 “+ Thry haben cope pled so ato scommodtealthe change madela EE Snecma 1+ Themotimprant pot hot ie ian abe ole mateo ‘hapa been dedi small ions ith eee each eon thn ‘ender wilbe ae top tough he lhpterin pena + Star omplton thar Seed Exe fal EE tps hae ben en. proving 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.
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