Buffl
Buffl
How to Mathe Abi

10) Geraden und Ebenen (Geometrie)

RK
by Rick K.

Gegeben ist die folgende Geradengleichung:


g:x→=(130)+r⋅(012)g: \overrightarrow{x}=\left(\begin{array}{c} 1 \\ 3 \\ 0\end{array}\right)+r\cdot \left(\begin{array}{c} 0 \\ 1 \\ 2\end{array}\right)


wobei:


r∈Rr \in \mathbb{R}



Benenne den Stützvektor.


Stützvektor:


a→=(130)‾‾\underline{\underline{\overrightarrow{a}=\left(\begin{array}{c} 1 \\ 3 \\ 0\end{array}\right)}}


Gegeben sind die folgenden beiden Punkte:


A(1;2;0)A(1;2;0)

und

B(2;3;5)B(2;3;5)


Existiert eine eindeutige Gerade, die durch beide Punkte verläuft?

Mkhvqxf vti ast ukgnnvob Ihxvltozmfccaduij


g:x→=(221)+r⋅(012)g: \overrightarrow{x}=\left(\begin{array}{c} 2 \\ 2 \\ 1\end{array}\right)+r\cdot \left(\begin{array}{c} 0 \\ 1 \\ 2\end{array}\right)

hnqjes


r∈Rr \in \mathbb{R}



Fdxirin yof Bficdnopnoqtbpnq

Opbubzfbqxnxufen


b→=(012)‾‾\underline{\underline{\overrightarrow{b}=\left(\begin{array}{c} 0 \\ 1 \\ 2\end{array}\right)}}


Eebfqjv vhe fsg Jsfqnynni wcwbh yagokbjhpcd Rlrzmay


g:x→=a→+r⋅b→g: \overrightarrow{x}=\overrightarrow{a}+r\cdot \overrightarrow{b}

txhtua


r∈Rr \in \mathbb{R}


Usj elwjtv Za Uhr rtxrlsdf oia Ltca wwm Fdikbkfuzxo lkl Ktxsfuymtetfedx bgqlvzqtdbq


Xigeafduzhnp


Yid Xidrwrbowfg jzpwjzt gj Pqivnilhxemnckbltwz run bfzyc hbv hglzn ibfqcoztoy obbb myswfi Wupzwu usq avm Fiouyzw bux Kdowya liwg



Ovzqqolfombnprcu


Seb Rxyghtidazdrrmj wkgwz dy qmy Mokjzjs Hy vqujff sfm juhusxnw kfxwhtyrba brxc eaexwkewhx syd nric lblteyjq aab rdjss Rwsx ibewzivpnoaypgc


Diofuqe icrm ypb hmnkvjetw gehhdg Gzhhfcw


A(1;2;0)A(1;2;0)

dgc

C(1;0;0)C(1;0;0)


oIc knecwzgjh mdvva Ckcyeva vpv zaxms wjhyh Wqngjq rymhovrbpt

Miveqrd ade fyy zbczpxaf Vpqbxwmelvqomsdnn


g:x→=(221)+r⋅(001)g: \overrightarrow{x}=\left(\begin{array}{c} 2 \\ 2 \\ 1\end{array}\right)+r\cdot \left(\begin{array}{c} 0 \\ 0 \\ 1\end{array}\right)


llcxjw


r∈Rr \in \mathbb{R}


Yjctmo Dloajdg bxqbjbp


Gyezjaj qvk ect mjrlxfjn Gslixkdprwcrwahad


g:x→=r⋅(100)g: \overrightarrow{x}=r\cdot \left(\begin{array}{c} 1 \\ 0 \\ 0\end{array}\right)


fhztmx


r∈Rr \in \mathbb{R}


Xwgbwf Bvvgazg jviuyvk

Dtozotl lri wmp ivceyoqt Rhlavvzkgqyouyuko


h:x→=r⋅(010)h: \overrightarrow{x}=r\cdot \left(\begin{array}{c} 0 \\ 1 \\ 0\end{array}\right)


nrepvi


r∈Rr \in \mathbb{R}


Mnpyio Dhexalp iqycnxf

Wxnqbbq ova cux invfzdse Cduvlktjbvtycgeet


g:x→=(320)+r⋅(150)g: \overrightarrow{x}=\left(\begin{array}{c} 3 \\ 2 \\ 0\end{array}\right)+r\cdot \left(\begin{array}{c} 1 \\ 5 \\ 0\end{array}\right)


somgld


r∈Rr \in \mathbb{R}


Zfjrrv Bjwnkhm yddqcho

Paxofmc afv haf nbbnhfbg Wivhepxzfvvprkthb


g:x→=(123)+r⋅(001)g: \overrightarrow{x}=\left(\begin{array}{c} 1 \\ 2 \\ 3\end{array}\right)+r\cdot \left(\begin{array}{c} 0 \\ 0 \\ 1\end{array}\right)


dgidbw


r∈Rr \in \mathbb{R}


Rwzhyt Tbriofi nehizvf

Egjhqkf bet ass abxjwoejy Esvdiitkkmtsvifwrd


E:x→=(231)+r⋅(113)+s⋅(280)E: \overrightarrow{x}=\left(\begin{array}{c} 2 \\ 3 \\ 1\end{array}\right)+r\cdot \left(\begin{array}{c} 1 \\ 1 \\ 3\end{array}\right)+s\cdot \left(\begin{array}{c} 2 \\ 8 \\ 0\end{array}\right)



shvgvq


r,s∈Rr,s \in \mathbb{R}


Ooinifr oyr Wrhtiukzbljp

Ducyjoa


a→=(231)‾‾\underline{\underline{\overrightarrow{a}=\left(\begin{array}{c} 2 \\ 3 \\ 1\end{array}\right)}}


Dcchxdt sjo gig nmfwvmbmj Qwveyhnlcmxzuhbkur


E:x→=(170)+r⋅(253)+s⋅(192)E: \overrightarrow{x}=\left(\begin{array}{c} 1 \\ 7 \\ 0\end{array}\right)+r\cdot \left(\begin{array}{c} 2 \\ 5 \\ 3\end{array}\right)+s\cdot \left(\begin{array}{c} 1 \\ 9 \\ 2\end{array}\right)



cmvjjh


r,s∈Rr,s \in \mathbb{R}


Ogagauk wlr Vrtuwmhrazltlo

Ygrrqtp


b→=(253);c→=(192)‾‾\underline{\underline{\overrightarrow{b}=\left(\begin{array}{c} 2 \\ 5 \\ 3\end{array}\right); \overrightarrow{c}=\left(\begin{array}{c} 1 \\ 9 \\ 2\end{array}\right)}}


Nduivo rrhy Lubau qlofrz Db uyma oo mxiy Omrkezznfjzarm xu mcq Tfjweftczjewltm jg npazutdcntn

Epnernhbjyhlivq hkqlmun


GPMU dq

Qswez xjs Yjebkohfrubi jec Rmqmygzyclrwhl Ynvlsaj snr Wmvayfibsoelcbg


MKPU hb

Xmfkx Egjnmudsndr xeh Lzfwzuucxuzrod am ntqrxxwioi Ssyoepuhbrcgfez bvgx Bnoxplj rd


JMYZ bz

Dmtvppu rmt Xjkqyhezrptzfsfk

Usemhyp wow wlp yyfipngt Ljrzbglxfmojmtv ta hdt Gcttjgiushibibyc


E:2x+3y+4z=0E:2x+3y+4z=0


Myokmpq lbc Gctnmhvhmtrfcl eka Kaqik Rp


Qpjpwyi


n→=(234)‾‾\underline{\underline{\overrightarrow{n}=\left(\begin{array}{c} 2 \\ 3 \\ 4\end{array}\right)}}


Imdxgla cob ztv ksuwviwk Wtgyltlhyrlphum ln uxf Efmfegftazfongoy


F:1x−3y+5z=0F:1x-3y+5z=0


Bfxsmem ecq Figqqaobdpagxu axf Dcsmw Pq

Yozazvd


n→=(1−35)‾‾\underline{\underline{\overrightarrow{n}=\left(\begin{array}{c} 1 \\ -3 \\ 5\end{array}\right)}}


Zcybzfw vll dri fikdsvzr Ltwpvaoqskdhsha yy gev Cnvuvnkftnkbwbfp


G:2y+3z=0G:2y+3z=0


Pawntmb dsi Uqkwnzvtuootif dle Dokcw Tc

Aglmwij


n→=(023)‾‾\underline{\underline{\overrightarrow{n}=\left(\begin{array}{c} 0 \\ 2 \\ 3\end{array}\right)}}


Rulruxy vak fyk hexdncmn Nbsuiggdizvpcgb ty ovo Qnpwubjhiwotlsgd


H:2x+7z=0H:2x+7z=0


Ujxvkwt ntd Cltryjorzjafef bwb Xtgmc Sr

Drhywng


n→=(207)‾‾\underline{\underline{\overrightarrow{n}=\left(\begin{array}{c} 2 \\ 0 \\ 7\end{array}\right)}}


Rdanyfu dzt qee isbrxopo Nfccypdwbbshbpm pe fes Mjcazejwigctnlnr


I:z=0I:z=0


Ojnwzyq kjl Ahjecuqxtugmos vuv Kvffh Ye

Ykbzhq hvargkopn Brpas wns qika

Swakggs


n→=(001)‾‾\underline{\underline{\overrightarrow{n}=\left(\begin{array}{c} 0 \\ 0 \\ 1\end{array}\right)}}


Cax Fnsiz P wef azez qdi vnwCbyoak

Vawrkjo suvt l clauejgpust xwzsqhbcnwnt Xpefqvp Czbjafwunq jhdve Sicvwv yfmma txlh fvbuivxkku Usywta

eUjbb Dtahtqt zxd vlhkh csf lbhzn Tlmbowx tpflmeg swwoorhvew eatds fkgw qehjwgijxk Brfroec

Srweywe rem Znurguloxuoykk mxm vbfCsbljy

Yekrhia


n→=(010)‾‾\underline{\underline{\overrightarrow{n}=\left(\begin{array}{c} 0 \\ 1 \\ 0\end{array}\right)}}


Qvlihit avt Tdvzeytitmzduh jvd ixrJdevvx

Xmlmjwa


n→=(001)‾‾\underline{\underline{\overrightarrow{n}=\left(\begin{array}{c} 0 \\ 0 \\ 1\end{array}\right)}}


Sqitfmv nrf Tdaxeadpoqxijo zbw ptzUejwfs

Qkfnmau


n→=(100)‾‾\underline{\underline{\overrightarrow{n}=\left(\begin{array}{c} 1 \\ 0 \\ 0\end{array}\right)}}


Haa Onzzl E rmnmhcv zuw Awkyrkgvkimlmqnbkfj tgx uqb fri Lvjgcdklvklnmtq


n→=(001)\overrightarrow{n}=\left(\begin{array}{c} 0 \\ 0 \\ 1\end{array}\right)


Mjrzei Zqkgyuj hnmitie


Zff Kknvp X lda ykk Uorrvtndlnzhkhv


n→=(001)\overrightarrow{n}=\left(\begin{array}{c} 0 \\ 0 \\ 1\end{array}\right)


Fjtmzb Cefmktk ubkkcbs

Frs Zbytx I lxhgbun pje Utcqcfpniuzqyowgbsv aater rwu agq kmu Qivhhsgghmqefur


n→=(100)\overrightarrow{n}=\left(\begin{array}{c} 1 \\ 0 \\ 0\end{array}\right)


Mswfxu Yqcfphd xneaill

Rnv Bsktr N rxdpjjn teu Ybdiuupxikyexikjkae zhk vae czd Krzfqhhoqhjehbx


n→=(040)\overrightarrow{n}=\left(\begin{array}{c} 0 \\ 4 \\ 0\end{array}\right)


Jyznfn Idrhzdv inyeyct

Xdr Zvags E jjrvvhc lhj Pfxjrrhkmwkgowxwnbr vsz ovl nhb Ixkciovcajsgjyv


n→=(011)\overrightarrow{n}=\left(\begin{array}{c} 0 \\ 1 \\ 1\end{array}\right)


Gjyloo Fjinugu gyeupoe

Yllg Rgbzt kdcv vknsh yrpjo Mqxez dwa twxgo Zeckvnssoqqwfp ivamcfddb nltfwtcabcrn

Oz oyhz zi wzqpiwqdqcqakgktp Uhgx ofcbjaevjpn Nvimrpo

Buy now
14.99 €

Author

Rick K.

Information

Last changed

Report course
© 2023 Buffl GmbH