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  • VECTOTES

    @ So,-uc,ont

    ?, Sunna J

  • @ sotucron A'= (e,o)6 = te ,,f1 : q-z,l)

    E = +'6+6 =- (ro g)t8[ = z-.iTr*= lf + tSvqt yqr9ro, h*;.:-:tcio, ebe- s"+i, "aorW.vL...uni{orfo d'qL vector ,..,Ii;**;

    @ solu"ton;nes{; {tpq de. ederctcrl}S E'rnere.es cc.art }.+q.ruo vrc{orcs togens o-q"to. ."rl-O""

    Px -- 5*,Rx= l2

    e={F=B ^--4

    6 solucton:

    ?= F+U.-z

    c.-= 3f+R'Tt

    -+4fi= A*9 ..--rE+dil

    corrstdercrncla J tr trreq de.todo'l. t er,itmccs rrt+? [= rfZ

    nfief = 116 [6*{snces'.

    il = nrr,Cd= H-ffid = .- El = rqr-)lFIr= ed = tsC-v?J

    Pe.crrnglqqn[u Lcs oF"r to.rntO ert ?lyL :q,rntLC:tecofts 6;y1 ft*+qr.*o 6z3r.isvr

    So\ucio.n te-t-l\.--}r,3Mi-'.*!n .---_{

    +: I+r1-\ it_- lo-+,F. I =-oJ

    t--_6vrt ---{

    tcs )

    -(-s

    0

    9.lrt'.t*Ir\Hl ,,;z-.,_L - - YZ:o,-l-V{d

    -zv ---l

    Rvt ------{

    ecu. *e trontgc & snr-croLrOt= A

    rJ.+V[o= .!-?s. 4 u"+=tg

    \ltrV

    {= Q=-69-vd.tVz. tBt={g-

    La grcquru{o.es cso*o cl"{ar,ro}ftEcorre, Las rnovitss on{e del EIE,A{= {s =f,qo = {fF* F = ,f Q,"aEAi.{o= @, loog= z_65

    6"{aes los u{omcr:asdr=(rrt)cz6)= tltr1-- (J',6)rA)= 3Zrrrl

    9!8. &+c- e.arclc^\a es gcib\e tcsotrer **tir,t 6cornc(rtc ges163 lYro\r\trs se ttr.tci:ectruYl ejO.

    @ So\o.mt t S.. hornbc aa,yruinq Jese .L pun*o O.ry ?om tos posscccs del hornLre .o Ua portef'if rno8 o,\etodq, dc. Lo sovtrbr

  • '.lrlrl

    ,\)t'p/?

    @ sohct:on

    Vp6n= H =rrq,Vta=

    S = Z.0cra/g

    vt 3q06Smt6'

    - SorrCrro-sl)

    JL=rev8 'vSu = t!s-k1

    dedtntcrbn Je:lpr. = itlon& tcsotttd{

    C,ie? '

    V?rorn = qtgr.rclE, & vCqdodcs

    = 9-F , cssna..*hdalE_ L1 Vccdatgc.{

    u f* n = $$ = .*k, e.,,*oAt .ht{g

    Pot [o t*d. sn4;cvt.I 4qg

    t= {6lso-6 O

    t= lO - {"OI?r- ff.to-' 36t=2,6s,'

    crnqsn J-*rh,meoc cmcuenHd=Qghar= q+z E.=

    ffi$o=+etm

    rogP'

    ts

    A

    't--l_ sm ___{_81rn-{

    f =. r2o = 6qsq_(J) So\ueron

    u{'r-l'sr.do Lo-."uqcien {"Ie. tiuwrpo Je ql,cons e

    @ *o luoon

    ??:

  • @ sotucioyt:tr , tz

    o--]o^,t-x--{

    -g -Jt, + t"z.4ZhRorrry\cdo:3t"+ tz tZh

    t= Bh e ntotrccs

    n-- zvAoticondo HeU

    I Vt, = 7*tzs6rt,rzitz.

    tt=9h,-------4

    @ sotuoo

    LZOOwT

    o

    ^;=;==3t--.--. --l

    Gatrdo cL trcsvr e*rovrxo

    d+roo=VVCat)+ lzocl = t/4q

    l2'o0 = 66Yu = zttn/s

    @ s"\^r.*orr

    36rrt\a drs.loncrlo tc.corrrtrds Por s[

    3'lO (q) = Lx -761360 = zr

  • @ solue.rtrVa6 O='l0tr,1(z

    ,----------L-

    ,s

    T= 30sHRV

    =-6olg * seo

    -4Ccrsderosrdt [0. euerr" ovnLos TrorrrOS

    1q'. S = q{r\ = 106

    V*=V;:rc*

    o =V{ -5{V4a 6t

    -JV*' too{S

    .A= \wfre-

    x \rz--/S

    * corro A+lrr$

    D= l?8* 60 = $gaq /y

    e= vu)+|q[rlE--*.

    D=vcJ - -i

    2"

    t0* = 6{.{=Ltr

    @ sotrc,ton\ qE

    A---

    v +=rsE* -_F ,retJG

    .qtc.

    NUV

    1 {i*,po {J.ltt.: 3O5' 3tr=Eos -) r.!S ^ tz=ZOS

    X= Lctc)

    (lol2- y = (oo)(ur) - t(sxzo)zP( =, BaOrfl Y = tooOvt

    ,(+ Y = 1SOO rv^ ./

    @ sotucrou

    2S0 a2-t =

    O=

    Lo- vetoc.dot

    .s- to. oHernlro no

    B Cuamdl so- emcue.'vrtro-\1 /err. la ptiTnero+tlqsrc^

    ?r)+ + zA* ++ ({)tz4ot + +Z

  • @:t:='l',I{ Et J *tqt.o J.- \o re",{.rct

    ,lf * 2'2-= v t * +'oo\f''. ffi=qfr*ctor;zLZ= zV+ + z

    qLrm porq ocrcrLr-. #ito'nvr-= ff.2x0r)"= fro)X

    x= 6m

    @ sotueion

    @ so\ucto

    T q -r ?oto 'L cuorPo Q-"

    i i i ^ d= )t{ -----rXl j d. Pcuc..l "*rro e! jI t flo d= rr+-tttz TI i u=*r, la eo+-iz

  • ESTATIC4

    @) solu.iotr

    5a"l

    co:ierondo en lcu so\ucq'fYl,a 2,6tt t YL 3lgEL sig*cmo ittne sls ta,Ptde3

    Lo sorro{otia. e iLo, :rrrtcrtta. de Fsc(gAS grr l,crdtrcceion de\ rrovit.l*.|.. < Evntem{o s F3OT= m"senn B

    ^ f= resor 3o

    ftrf,ScnrS wt?se1?o"

    D.c. L

    "l-'= 2T+P ^ T'=FEKX

    6 = 2m,Q*P20ox= UCO)ttO -) X=,25rnr.2 ZSctttt/

    : OJo/ ecotr'1orn LocgrrcotsntlZ - 1I= 9oN, P= 15 y Q=14

    gE

    R6f.6)=sq4Bs=36hl ,

    () solu"ion D-c. u.

    .^. TtS= q6OO => T=3OGN -(3_Z) sclucion3 -:--

    T3rl

    tr.

    Poc.Lo Seq,rndo. condtclorr dq equi\rbrt6 ccnrcpectoq0f =O.+- .tCa)= Oar,

    T'15 = so tto) + 20 Ctoo)

    Apllendo Lo. cc,rdrrebn Ae equi lib'o

    &aiF=n ^ JJ, =zF+3Luqo:F+3+F 9

    {Fa 6 : F=7 = KXZ1=lSkZ toc''

    l(= lS !Lfn

    D.C.L

    T/

    a,Por conis\no de. q.rrttio

    $.f^=O s 2l=oE = TCojES. P= fsonS3 "

    I{OTA: L sotrcion qE-tercici6 -vt Frstcadege

    D.C. L.

    For quilitrioT={= tE N= ?coe9lo

    f+-- ?senX?a

    J =16 N

    D.C.L

    fu,$'.

    u

    -\}r"

    La sumodonO

    T=Vr.$ LvaXo'"

    a

  • @ s.,tuc,ton

    @ sslucfon : aIunF - fln[-I+Fl--+

    dr.

    ffT= mtQ. = m]( fT= LF- t"n crr+tl

    ?t +l

    f{rnru-"zn*nA)G,0.=F.

    r(n+ " {+1 JCl"= 3f-

    mn(+I!

    1+T = Fvr:f",tl +T: g5o,tlf '

    $ PCgllo+.t?c f So.r:)tl".tl:t/3 ,

    -=f

    Yrt.{-f = m.Ov60 -T= l.z

    T= rleN

    '+q9"1+"n&

    N = fl.gCos3?"w= +o(1)N =:"_

    ll= O,5 .--------t

    I

    r-

    rr.L -c UtTcos 3l'= nQT= 1rn2

    CoE3f'

    O solu.,on trrffite

    {={s rrP

    t(\

    ?ot condr,"cion d.l pnob\cm4N - p_37.p

    . N=BgooAelicande L. Zda f-f .1. err*cm

    @ Solucion Lu.(o.m\qob" JJ p,oblerna no tltclootll, -- loF "

    rnr= 6Kpvitr'ortr d,u*.:) \f= stfzm/"

    @ soluca:ov1(^

    !u,I-.--.

    r. J

    x{ 16' xnq

    ee Y'"Nc 16"= mq.= ynQ.

    Co: t'ffI ,.1

    n eLee x'.Fn- = YTIQ-

    Nen16" -- mO\IrtQ tam16'; fnC\

    LIO)A = ( ->qNI*

    freorlt'

    T- { -}nrg&m}l= In0.{8-.ru - uo(e)= rq)()1r-rrtaz)-4\=* -)

    @ sotu cr'oqA

    ,,.-@--..,' l"(\

    O so[uctoyl?s-'t = Qft.+fig)o.Yn6Q -t"t N z (r+ me)tlYrdro) - tct z0r=

    q (12)+ rrn '

    6 fi6 = 1g + rns=13K9

    {=rrfrr= JruJ= (16)

    SJ opltcorrtm utro,{te6a-P:ON, erta pue.rgct'q, e-apos dc Fls+rirtsvlrtcntu P

    *= 96

    solucion

    t-."3e no Proice movit"e"*o P=Q

    }1.l,>ytrz

    O[,?

    Fs = mo.g= Yrtlq

    rh! =rnYX= n; =+ v=6r/S

    La gteqstdo. &tee craL cs lrvetot rogtdca cort to.croLPodria, atar A.. sera- merrrr euorrrclo La. torrrbn efLa cr,retda c. cer6 ptrc\ cs*orr qetnto & ^aet-tr trtol tcwte.

    8n t* e4e Xi lurtc ^rrurt.Tr. = mtreK-

    TSon)fo= rnt ?(thq srh3i"

    = yrtrBcc3"16 13\=Urzl

    tq I iE'@ so\ucion

    {000-3gOO = coolL60

    a= ftrr,lsz

    Aeltcar"Jo Lo s.q".da L"g & p"u{e rtoL srs+srra dc.rosas A90

    f-= 1It6.firt-mr9=tmtfla)G

    lI6Q = em'6&'* i9 $lsz

    Fo. rnov. rtBov.' V"= Vie+o'h

    ,"= "(t)t -> V{='11o4

    vr'l'-l-- t .t\t . .l.l q'=sorrt'

  • @ sqtu.eorlnptamdo lrq. 2do,. Le Jc ew{oaaL sts*cmo dc mosas i

    1n' = mO"

    F + P5 -?" = [ntmu*m.)Cr.o+ 60 -t6O= o

    d--o)sYr./62

    mq

    eh eL .t-'X': Czro 1.9d. \rs.{orfFr= rYICr.

    N = YYLO\/!-2. = mgr -->.rr'

    @ .otuoo,

    s r6{pT= cslfil-E;i-]-hlO- 5o-sh

    =2-6hr :) [=1r6m

    D.e- L .

    tr d e,e V'. F"=6[N = nrrq

    M= B-,rt

    l-Q- = Q: tctr,t/.2o,L ---:v

    rrtq=sSot9N= mt,

    SsB

    N" ra

    H*

    Ap\tortdo ?o. Le"e $eurtzlqL srlTT^A de noeq-gFr = rrtCL

    F- P, = (n,.rwr) elSrgO= r(

    o,= {m/"2

    A apltondo to. ?Jq.C,orndo eL cottori

    Tsqn EEP

    ,.=to[i?F-

    J,q@ solucton

    @ solu"toa.

    e ',

    6r, lo drtocelon dJ .e.x;f = ynorzP-

    NC.Ae= mrrtE. -hlnq. cSg

    = rnr)t(. :QMI'

    rr?,>o o"'J:;..X.*go.rd= tt*r.

    tL teasns p,,aLt,.,noc) ,r" j;'"u$* fo?s* esuvr rrat{.o c.,n ofrcrSi}rn oL rnov.\^, =-(36) 0r6J = : l" S_/l

    D,c. t-..N tue-'a

    h\r

    /2' .' ?r2p a$=k 5b-

    @ sottrctovt

    r"

    @) solucon nos prJe. colc.,tcr \7.% - ?.^ = 2-5'/' ?4

    & = t --) fL'h= fr**''gs s YY.=3^Lo=86:

    1.e.1 e eurro"lSe qnctgt*tAgyr B

    Fe=YYLori1t?-F= Wr.C4lo-xx.= t1t{0-2F qo.

    4=6m/"2,--------7

    @ sotu"to'l1

    ,.Et2

    '1 '-

    ULt

    E= EG

    hmg = ** vo'3rg = 'Ir.o'

    vB = \r[6

    -_+1

    - mZ Ssvr 30" = tvl -E-? = 6m

    N= t3n2z

    N - 6.5mQ._--a

    g2r

    @) sotu.^un

    V= er{5------

    lrrel T14 1r/t > ?23 4'7/r? a42t ryl 't-- d

    ---{?o- l-1RUV

    Vt= Vi"- eoo -- eor=- zgP

    t= z0rtrlPs = LS kotl5

    '---F Pt =rr = ELz6'a)(za) = E

    E = Soo f'o]-h ,

    CInt

    $v,

    VrgO

    Pc. "ot

    s"tvocicn de Enetqiq

    VI = t{506,J

    soo = F"(6G)+ (roo-f.)zo+ !oo:e)C.oj{50O = 6oFo+ 006-zofo+1oo}-ur.

    lSOO = z6 F6f,=gON

    eo xtr)

    Eo?ot [q sonunJa Le.o A'\'lcuncrvl

    f- *q^m9 = mO.

    { tf

  • u --- B.

    @) so\nrcron

    O=3f .

    'l

    D.C,LArss"$'l ,/rd;

    f Ts6s3oI+m?

    D.c.L. tu.f

    Ifplo La a&, ti.t de.'Fe

    = tnt"Qf = UN=,t{1yt2=fntf (

    JL?=t'2(3 [to)= (o1o

    &neLqe I ITvtf = tr$'[e

    N= msm0

    En eLee.;tlfc.= mtoR

    NCs= rnrrzR.

    I-g'= mrr'h{ge-ro

    ?= \^zh {5bto = ts,z,, ,=-h= tzm ,

    Fn=Q1m9=TS,'S3o

    , t= tyrtScs3

    P= amE

    NetfuV\

    T=m[ZR.

    tn= Yv87

    vz= nJq

    \azzt!a*z!9 =*z4-=r

    6'.Jee- xi ,F = TYutI'P.

    TCos536 = n t?R-IttBtam3{" s y\Uze

    t0(-1\- r.^rl --+ ts=6ro{s\J 10Lo- \etrBerdad ornqulot- voemo

    @ so\u.r,orr

    tsu=

    t -!md/s

    D.c.u

    -1s/*u*^"4^,

    qh -* f,= hfog

    @ soluctonD.c"L

    .b[ *e'

    Por H ArrV

    -#=o, u [ur=o

    / sl- _i-D(

    x_- vc = J-R?.|Gv2

    @ sotuonnxaR- -J

    r'.dl.Se i'1 F*=of,-z F&nSjo

    I t=r.o =.*t --- \n=66oII

    Wtr = tc- 660 =