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e _UniE No 2 _“Nectors And Eq, gilibah + ‘Topic - Wise Questions Qnol+ Define sca Lay and — vector quantities with “eaanigles 2 Anse Those = physicad quantities cuhich reguive anit aay ar Oa candice is = escription 1S cae ie? Distance, Speed; Work etc. Vector Quantttes~ Those sical —guantiter which reguire nitudes unmet Gra Viveckion for Hs descrighon is called vector guandi fics. Calis r velocity 5 torque etc. OAy ) ey ere pn Diffrena ‘bhs scaday nel vecbr © guaxtiticre Scalar Quontibies: __ Veclor “a | < cal Quantrites cshich 1-Mrose physical §— quastities which whose | physi es mapenece Gun lancom or” scription iS called) chesaription rn Rehan | "cae he P | arn ee a é 1s iat i Simpk2- is yepyesended x a a | @yaeg co anel of : | rtadic Cuords CA 3-Scablar Auanti tic can be 5Ve choy Quankles 9 oe addel, Subbtracted, vacbtiplied [ added and sullwacted by ae divided simple | Mead © har Yule oy i iy Y Lau Adiko gebric method | ( paraletagram — Caw addition | addition’) . Keep sonal g- = a 1- Speed - Torque 2- time |2- Dis lacement 5- distance 5 Vv loaly 4- acceleration edc- © camscanner —, PN re eff Qnede How we can represerd a vector a @ Anss Representation Of Vecklors. We can — represent o l= 2 Vector is a Head — Me ened uit of AVrow b . AI ile 7 Direckon FF Wer dg Th ectoy. tne divectiar a Qnote Ure coordina Ea with its types? Ans- Co-ordmadLe 1- 2- — Vector by {wo methods. y Se gn balically a ba is~ vepresented — by ay bold Claes leHer (a, B) and is. Tepvesensed by Simple - Gaca lettey with an AV Vouw aloove and _—Wweows ik Uke b> g ede. words Uke reprcterrkel py italic Giraphieed Aapmseseiliin: Gwaphicalfy a vector 'S Yepvesented — an arrow - U ede \ead ee wedi: nog a” Tail Tail The Starting point of vector is called tail: _ "9 poind f veckor S Called “Give Pau Veda Tr. length of Arrow —heagf Show of a’ vector. Dede A sys tam wives have one oY move vunver to — dekermnne Me position of Ppoink = in space S called Co-orclinade gystem, baad of Co-oralinate Qystemer ave two types of Co- ovdinade systen. Cartesian Co-ordinate Syston. Gieo graphical Co- ovdinate Syste. CamScanner Qno5- Ansi- Write About the {ypes of — veckor 2 @ Types Of Vector: Following ave Some {ype of vector. Parallel Vectorse Wise vectors whose Line of — action never = cro$$-— each = others IS is called parallel vectors. a 7 Une of action wn Tupes— Th ir, gis af pea Like Parallel Vectors That Type of pavallel vectors whose divection = av Same Is called like Povallel — vector. The angle bij ike parallel vet tov s is O. + 6=0) Uke Payaldeh Vectors - Unlike Parallel Vecorses type of pavallel vectors whose diveetion is oppssite to each other js called Unlike Parallel vectors. Me angle bhs them 1s 1 8 O°. O= 18 Unlike pavalled ~ ‘ Veckovs- Free. Vectore— & — Vechov vohich can ye disploced parallel to utself 1S ca Peel free Vechov. Condition— Free vectors ave not — concide wih ovigin Tal co-ovdintke = omts- - Os . ° fee Veo w- Gis —= $8] CamScanner -unyshs FaPA0-92 — OIHADD_— AQ}IIA ygru Oo moy4s pP sy 7 sw-vt | swo-F “ayy Rs Yyeulpad - 9D UDIG>2} /DD ul | AOPoh you v omy) uvD mi ez Prong 10 5p AOPIOA yu fo wipe wl ropa fIV fO uorpesig | 4 oy pens. St hy apn} Rous _ BSOyc? SAO a/A 2p ry aSoyn VOPIOA eSOUL =Pa -Sloyan anyobou pou DAD OPN pared myn EMA SEPA A PIMC — mur iS Pye) - O8T “MOPIDA of cc DA = rGoyus S) apnpugou 257th aye Pret POD ny -h “SADJOOA pemb you 240 von pyrened = mi EMF yoyo porrrod TAI] WD Yoxran porte “? ah & “* al A 1 StoT?9A < puo . wos per Baa art yopan 24 490. -wO & (C-7 to = AQP DA sro we ——_—_> —_—— spsoddo sy pan wppo PUNIGO § ss sapan gm a AOXP\ Rdur P2722 FFD i. = Z a you p2yy7? SI OZ Ss! Sssopaj pop | -¢ YOPBA MYVoOIU uD 2m = harnqo Ss! weaut 4 ajbuo 2yy . MOVUYO ou = peyyop SI yore s1eoddo fi 7 uoryre Alp page| 2WOS Ss! yor P2241 P apnyiu — IA yon by ie “y TD ~- IN H + Invynas Htanicn + | -~ CamScanner Jo- JJ- NM 4a. => Ika magnitude of position vector Is be Drage Psion Vector A Specify — the raped to vector which IS Used to¢ position of given oink with origin iS callecl position Vector. i Co-lineay Vector Those vectors which ale lie on the same Une iS Callecl Co-lineay vector. volation 1S in the same ve ctor. Two vecdors Co - initial Veck: Debs havi Same co- initial ve to each — other Co- amial VeFone votationa) effect Enamplese Angular Porque’ ekc- Co- planner Vector Those vectors which lie but tivrcl — veclor in the Same —> Sew = ae B Cc O Those vectors that represent and at along aus of abled co-auial vectors . Momentum, angulay velocity » plane is callecl = co- planner lie im +e Same plane m or = =mag, — not lie Plane - “6g Cc» i_>» plane : Ov— When lwo or | more vectors Stavtin ont is called dors. dg? Co-mitia — veclors Co- initia ~— vectors having angle bh, themselves. wr Ontiparath) § perpendicular Nol pavallel 40 eacdi other CamScanner Jo- jJ- Poston Vectors A vector which (Suse °@® specify Me — position of given — point — wath raped =iIh wag of position vector iS, pe pe Co-lineay Veclor Tose vertors which aff lie on +e same Une 1S Calle! Co-lineay vector. ar B Cp Co-Guial Ve ou eclont— a, vectors that represent rolationad efect and at along aus of volation 1S abled co-auial vectors . Lnamplese Angulay momentum, angulay velocity , - torgus’ ekc- “ ag Co- planner Veckors— Those vectors which lie in the same __ plane is cafflecl_—_co- planner ve ctor. Two vecdors lie i +he Same lane but Hw vedov m ov mag / not lie in the ~— same _—_plane- Co - initial ~— Vectove— Oefe— Navin Co- milial Co- mrtied Co- initiad to each i to nitude origin IS Cabecl position veckor. C3 54) same ve clovs: veclors having angle bi» themselves. ve clos ave other plane - When dwo or yore vectors stay ting pom 1S called Gndi paral) § perpendicular bud _ Mod parallel 40 each othe. CamScanner 16-| Resultant Vectoree When we add two or vector Called resultant of inclividual vectors that added - R=AABIC. A Representation “«.7Sa]!——_—_—~* Qnob} LUhet is heal to tail rate 2 Heal To Tail Ruder with the fail of 2" Vector the head ; Ff 2) vector with tal of 5 vector and So Finally Concide He more than two vectors ge a New Yecko Effeke The effect of resublont vector is equa fo the sum af effeds Resullort vector is denoted by R- Definitions Conorde the head of 18 dail rejutlant ve cho wth the fail of Fis vector ond Concicle the heacl resell tant vecloy with the head! last Tis is called ~— head to a Nde oa ‘ aN _ eT = Sw = c=-S$ we ave veclov and concide the on. $8] CamScanner Qhok| Ars, Quod Ans:| y Im arfances le 7 add or join two Or move @ vechovS by head do ail yule we obtain a single Vector Known ah resultant —_veclor. Tre effect of resultant vectov is egual fo sum af the effects of — individual Ve ctors: —_______ a A Can we add zZWo with nul vedlore Ra | No, we do not add sey ith vector because — Zevo is ° scaler nant aud nah vector — ig ecdoy me P And — alto we add onf tone GHantities whose Pro perfs » we can multi ply — parkity ae 4, a scalar uankit ae “hi ed a — quantity new Uanit Alusays a vector 4 gia a . Fvomples- + The product of — mass (scalay quantity ) and velocity C vector quantity) Is called momentum “( yectoy quantity) - ZZ => P=mxv Tha procluct of mass and ace- leration ike force - Force (S a vector quantity . __* $8] CamScanner e=0 A-B- AB costo) AB = ABU) > AB a Bava ble} “ii Ihe scala product of 4uso out - Parable) vectors is. egual to negative of Product of. 5 their yggnitude- O=1SO" ne B= ABcos . re ~ AB = ABcos(18o) AG = ABLI) > -AB * geld fs Syual) te nr Sguave their megnituck 2 ff a id , rd vt = iicas€ A.A = AA cosd il = & cos(o) A-A = AA coso) tt =a) A-A = KA G) et = 3 A.4 > AA > i-¢ = U* o 4 Similar pe a Oe. imilarly , Jd = and kK =l ic. 'o | J Ly = Yose T Simi lar|, 5 ig = Yost) | J tg -y | j-K =o arG| = Jo d; -E = 68%] CamScanner WIS 4— Re Auc + Al 7+ Azk a B= bui+ a /Bzk A-® = Ans Ry) +t AzK) - CBuit Gy + 62 |e) fo) fa) *F AB = CAu®u)¢ Lt (Au@yt-g + CAxBz)t- e+ Luba Fe + Cy ey je jet Ryder pe —_ (AS Bwtet4 Lass Rj + Wz) E-E AB = CAwGa) + CAYRY)” + Az Be): NN Dede When we rnubtiply two or yore than two VectS 5» we et a resublont if He resultant = ts — Veco Quanti then the yoruct is ALso known at vector product. > Vector produit is abo Ged crots Product - vector X vector = Vector > Y two vectouw A and B ao multiplied such that thir realt is abso a) vector C, then SUCH tye of vyulti- plication ‘sled a Vector —radluct- Clsually a Cross (x) ts place «Vl tue ve cto. to represent ; thevefve it Is alse calle! = _ cross’ product. Ax® 22 Ax® = ABsnOn = Where 9 18 the smallr of the angle hh the tain Vector. (a) © Self tadlucba The Scop product of vectn A ana Kxk = kksind Ax A - AAsind Kx€ = kk sin) Ax A = FA sin() Ext = kk ©) =0 AKA = AAC) _ ixt =o | AxA =O. Arg =0. Mette Sat ade Aa ji Azk | > = & = Bui +B + 82E AxB = + CAut Ryyt fe KY & CBW + oi zk) t dg & 7 s e ok xB = 2— Az CAn&e — Az Bu) tk ‘ne rahe J Rr D4 c > Noy Cr -> or > A> AD Bed Cpe» " \ o> C= * $8] CamScanner lol0- Euplain addition of veclw in con- nection wtth head fo fail rule. + Addin Of VecForse Lele The process in which = we add two or More vector to obtain a singl vector is catled adldlition fo ve ors. = fddition vector sis aah peas Siu Vectors Wr e Geometrically by Arawsing them to Common Scale and placing then, head! to fail vule. Joinin the tail of fut veer ~— with head! of last vector will give another md which is the sum of these vetton callec| resultant vector. ma Situation of addition of vectos Is Simple for like and unlike Parallel forces: _ > fad the Mm, SRIEE Vectors in Case of like Para lleh forces. Cage a SN 10M Cate [I+ Subhact the nitude. ” of vectors th case of Ini Parallel forces. all ION + en] = fen- $8] CamScanner > To add these vector , we we head to tail rule 23 ~ mentioned in _ eps: » Such — that the tail of vector & is on the head of vectr A. Joining the tail of — fist Vechr with the. head of (ast Vector ctl give anothy vector which is the sum of thee vectow called resultant _vectr R. => Ihe _ —resblank - will have _ the __ S3ith. _ effect as the —_ combined _ effet of _ — both vectors. Veto, Addition [Ss Compu FoF. ee Vector additian ob dot Commutative Proper Tt 3 e the —__ Order e in ep wine ra _ave added "as ro Pig sical Sean two = Or ~— more —vechas are aclied fegetter _ theg. _ they alh have _ Same nits and ed must be the same iy - Quanti Yy . Addition | a 4 6 =AtG—-B4h Vechow. — _ The rules for vector Addition can be —_ eutendleof to any number _of vectors. So Sana ales Consider ____ four vectors A ; Bs, C ad O me t pra . 
