From 6d484abbe3552b6f75807fe75ecd1af2e962689d Mon Sep 17 00:00:00 2001
From: fruitstaa <dennisdimov@yahoo.de>
Date: Mon, 12 Nov 2018 11:17:10 +0100
Subject: [PATCH] exc 1 theorie

---
 exercise1/Theorie.pdf | Bin 88965 -> 89039 bytes
 exercise1/Theorie.tex |   7 +++----
 2 files changed, 3 insertions(+), 4 deletions(-)

diff --git a/exercise1/Theorie.pdf b/exercise1/Theorie.pdf
index 195b75bd03cb46f363c71297113e5a717e6fdbb3..0269be9c007d2407eeb472cf108f99803b76de50 100644
GIT binary patch
delta 1426
zcmV;D1#S9;w*}9)1+Zil12Hi;lQ9Y?f8|+Aj~qn|zR$1d<L1z&{3w?T6e-yV4oDn;
z6_=0$+9VQ)BtVeZ<k#bw>3MXIXQpST_klQVtJht&zxv9bU2}Og`{Eno1`%q`)Lgx7
zP#A=BQ;4Ckzk1!gy!ia&)z!CdDNTV|63z{?n_1H$l*&u1pA+lS5cBqu2A18&f5z}>
zx19AHGbmvr1-Nu}X>Qk~rX_^jh4L)&fC)sgL4xF=_rFB}5shAUmKa5o7csMWFuG+n
z2<CbBX&NMgSlkXWu7F9@S@yA>KdP^}u=*ne*-Gw#d^5M2eSJ0ibB6w<dv35GuoT}i
zh2juizni^$m73T7PY)QRSo6=qfAn3GJt!*v_<Qr??EBf}eE$bf76UO~3^U}_{$rG<
z&GSoJ8MZ`p@mrW^1}e8nbm-I9(Y#Hig*zv$FH}4tT7{FtUG3r^ah~8&jtz21pjdkx
zyZ-PoWTOI>x`8IAXgz`XLz?1%EqAJCn8Ph|oYW83X4AsRDo|aA|MA!Ne|vJ2njbvJ
z)|f9s*R2&WvHtmg+{r|wtH88&dVp{C@LPezxjRm+7Et41@ol+On*XJoG_Jdqyzttx
z@Rp;6cYuQ{meF?MeHvm)Ahh1?9|9;0DlU<bK3;u>Q5ImwpjB76(z*N;LR*sc7CbJM
zGEyojC}Uox&euxZE1)N8f8{EgqhdKmE%PxE(J^XCQX9<*$<_C4wPf?fM8LHC*VHoM
zc)dJTE;AtWv~sytu6>8BjILiC)i07*OE`n?*kp=0VH%-`xb`tr(w*|_Ww$sxeebBQ
zGfn-PmORzc|MF0uVAG>=zkLGxkvAKmu#bSE!3h;`;kmt9;yAU`f0NYm(;l@{FGtc>
z%bQ?51@%uJuUg{q$?{Is(k4{P5woQO;P7V4-s{l0YUynu`(j00d+2|ymLr-n|4Qqk
zZMMpX88$?u7MZN1t%dK%VLhXy?GCB*Ktt;JIqs2UOx|u*>R&zW+df0R_ta!;YVsf>
z>)l1)pFe?h?6u#0f9dH>sHa$*C*sqmcQDmDzI_))=7t-tOf?gSHPr2Cfb$r6I;pJ~
zI8@i1yK(qA?2wTwn0Jh=WcO`H4nt3zewvqbyLfZ`_lLitjdI?p?rf9=^x0<Uw#X#u
zxOcgFS-i}1@J>eA>59wG_E4U!G?KumYd<wYVcGI@X?+=He-5-c>P%cjQ&LNo)t2?M
z0;b#-KbpXoD@`dy=ND3(GIzC_7Wc!u*CDraw(exST3ME=DXR!(>h8)M`N2Kq6etQ)
zl3KGPX(>Xn(;%6^S7CI(GMjf$k|ZpwY4O{HI?vR0OY54rF9Jfo2#9;cZcW_h@tB*v
zpIa2qyrA$2WQTa%c>4B9i<mBc3C}tDC_>Q>Vh5CB)!5>}##Z7nDGh&rYpGbwGIU@z
zec^FV4`}vP*sHOhr+ONI@887OIafsP1Uo(jJKT$%oltzDdVuWg@G+THp{|C3yqe7Z
z1-W^VYlEN}x1bpT<23^@HZ+%pPXQnUF*Y=}sZRl-3Q|HrLpC@!GB7nXMMgA6LPJ7B
zLPSJFHbg@?Mm94>L`6OzJVHT3HaIsjFf}wqMl?o3LqbDBL_|b3L_;}7HZw*<MLt~$
zFHB`_XLM*FF*P$FlQ9Y?e;vw64gmoagyE{D4c%tlX!EeLwvxC*Tf2r>inxT+NL+vm
zID;z)soH$`U*!S7F92c+5NJX*6LT>ULopHyF(vm`|1Cv91Vni87K$PfWj@EEEJ{R+
z-m0QPq`A*X#G)qZq9K~1CE7&x^>c^Vu3cT?n7R_;c6X)3>*4AV7@w!BPbMeVfZV)Y
gnOKqe8RTJyKb-gw>6cww0UioAGd2n(B}Gq03Pf|kd;kCd

delta 1347
zcmV-J1-$ytw*`f_1+Zil128l*lQ9Y@e_6q98%GSi>nrBy9K;SeB!|-=K<c196zHL?
z(My^`;UqwTCTW`jb@KJ)YFCnXLs^o&a*QG;FV@^4`S{4kU7cSnzWR<zLWCwl>Ed-l
zF2F@nr2@71t(WQf*~dpOF1~k5P8C|s*cpnOSz030R(h*nbJ5-q<@%8ZChlWvfB0lL
z&PI+4C}H9Xr4Dwvvr9QG2|<QXo<<%p11lyZ$R7ImS!7_==;mOFQ8coOxtIr|*UTot
zd^0?nCy5|dw*$d7FqsC+G1lFs`k5=MKSPkM$_V7E&T8@P#p168`jhTCVMQohy<`g2
zA-sIEc>W@%m;O%=7`R&ccV+q}e~AZ0)i3`@KQDe<oOkt~Kxqh;Emahdb^S5Q)4Kff
z0U63IGMqZ248)Wgv@P2ttenS9UNd6n0`BF}B-{*&ZN#I?cke^SDPV2e^d(2<F?1Js
zjwb4>F*1~}EKY6p2HF-TjI05*P5AGBf4d_`Zt~f4Tv{n-q3fkpFt%}ze?RPGBGNS|
zv~hX^-|X|30;$N*PD`zzR;B}XS!$#1FG<#Twl?zNYW;Andxz@;2UjJd>%;X)h$#Wn
zrrJLRP#84qk>D|2V}_CNYGN+cRjdv!KZMZMTt^4)mqR{K4k;L8KBnf@L%qEouA|v2
zi1(+6h@4auvY&TnMHKg`f6QQ7AD|-g;fnYG1aYHHd)nxKA&9$jJe44NgWAai@f6A2
zpCF#36eB@2$W!n;K{VuE5YcuBVgb@}2SLQc1W}I?#1A_JQK5LJj0Ev2I8Q<SkuQR{
zOAzgFL6jK;(E)IH#l)*ecNN6E3Q8&iW%?qBa|z;}HoAX7wAlplf229yAc)OLQR~ct
zcn<};ogg0hMPgU@Wi~}@AeqOX+g6I$O0S5rOA$MYwnM+a-IpR>g%rc;1BxB9;$zVU
zEPe<hbHgpe=6Z1rhoRdOrIGj^GJcO*3?>fMRpT@cKSmChSQ=QjZ?U*<+tWh*$RE7^
z;@tCP?A7Hz@BWSof91SW{iIM9(C0csuZu|LfqUoco7LO11o!wLJ6&`6=?=;ltBErh
z4GW}3DD+Fqkk;2>=0Mx|P^eVaoYk_4THn(RFw1zL(hR<|`kb!XeKjgsO7CkWvlwq<
zw{W)EMSMb=aMLXQQjbEzv~uJp>-!uia-qzvi6dz_LU9<3e>{V)TF?QLVx+>E!_k^o
zKN6_(OzqRrx*_hffRN7u;_k8A5I5X}T>{Lvwr+UJio!=U@nIi0U%Mh<KKm`~bM%)9
zihh~8K`GW7D&DxEa{Qu`r$2-(sani3bYQl6zMs<*nmrD8y5jxRjsx)Rs~9`y3iC;@
zE5~4mJF&AP7=}+Y53o2pe0eFV(ALYotlzEv1B{<`8H4K?x9b@J<23^?H#L{hPXQnU
zFgG=~^iKhz3Q{&iF+wv&H$^!zMnN(-MK&-oH$*ZuMK(1uGBGkkF)=<MJT^ozLNi7;
zML9A?K{7Z+HZU<aL^3r+HZ?LbF)~9jF+N=iFHB`_XLM*FF*P(GlQ9Y?mk?V434bcI
zq1&t*Z60=(B;por>lnmdoWRaO97Ey?PGI8%q-yi!f0YLSzZ?)zfItJPshEke7>J>m
ziwU{k`fnlfB1Z%lZ-FQfVd`@vN}@<K>8&ElM3VUoMI@@CChDRgnxaLd4?nkw-P_e6
zPES`%+>fq=c%5Bc;&XNN$av-IlMtJmD-}yJTZ24&@dtBx5UrP|TLB&lH8wE{B_%~q
FMhcI%bEp6S

diff --git a/exercise1/Theorie.tex b/exercise1/Theorie.tex
index 0ab03ec..5a6ecf7 100644
--- a/exercise1/Theorie.tex
+++ b/exercise1/Theorie.tex
@@ -120,7 +120,6 @@ $\Rightarrow S \times T \neq T \times S \Rightarrow$ does not commute\\
 \begin{pmatrix}  \sum\limits_{i=1} x_i \\ \sum\limits_{i=1} y_i \\ \sum\limits_{i=1} z_i \end{pmatrix}
 \end{gather*}
 \subsection*{c)}
-
 \begin{align*}
 L(p) &= length(p_x - ((p_x \cdot (\vec{e} + \vec{d} \cdot t)) \cdot \vec{d} \cdot t) - \vec{e}) \\
 Vector &= ( L(p_x), L(p_{x+1}), ... , L(p_{x+n})) \hspace{6em} n \widehat{=} Anz. Punkte \\
@@ -144,9 +143,9 @@ e = \begin{pmatrix} 5 \\ 10 \\ 5 \\\end{pmatrix}= t;
 p = \begin{pmatrix} 0 \\ 0 \\ 0 \\ \end{pmatrix}
 \end{gather*}
 \begin{gather*}
-z_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times p_x} \Rightarrow \begin{pmatrix} cos(z_\phi) & -sin(z_\phi) & 0  \\ sin(z_\phi)&cos(z_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_z\\
-y_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times p_x} \Rightarrow \begin{pmatrix} cos(y_\phi) & -sin(y_\phi) & 0  \\ sin(y_\phi)&cos(y_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_y\\
-x_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times p_x} \Rightarrow \begin{pmatrix} cos(x_\phi) & -sin(x_\phi) & 0  \\ sin(x_\phi)&cos(x_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_x\\
+z_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times |p_x|} \Rightarrow \begin{pmatrix} cos(z_\phi) & -sin(z_\phi) & 0  \\ sin(z_\phi)&cos(z_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_z\\
+y_\phi = \frac {\begin{pmatrix} 0\\1\\0\\ \end{pmatrix} \times p_x} {1 \times |p_x|} \Rightarrow \begin{pmatrix} cos(y_\phi) & 0 & sin(y_\phi)  \\ 0 &1 &0\\ -sin(z_\phi)&0&cos(y_\phi) \\ \end{pmatrix}=R_y\\
+x_\phi = \frac {\begin{pmatrix} 1\\0\\0\\ \end{pmatrix} \times p_x} {1 \times |p_x|} \Rightarrow \begin{pmatrix} 0 & 0 & 0  \\ 0 &cos(x_\phi)&-sin(x_\phi)\\ 0&sin(x_\phi)&cos(x_\phi) \\ \end{pmatrix}=R_x\\
 M = R_x \times R_y \times R_z \\
 \Rightarrow Vector = \begin{pmatrix}
 6.323746006808568\\