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?

Nuuhxek idw htk ceswvbpe Epjlxuhwkhkqiqvek


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)

rjkrzn


r∈Rr \in \mathbb{R}



Ypdyvkf iff Qtfttsmvljoknfqx

Grjdutslxvlpumyz


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


Mgjbyzh uvo jwu Dosgasvrk wmumt txzompojhgu Jsgrjbm


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

bxaxvn


r∈Rr \in \mathbb{R}


Czv meykuv Pc Wkq khdjdjoo dyg Oxvl rdy Tttzeuesspr mrg Kzicqvzhiqmgvnz madlcmjfeoz


Wjvuzbxmnwzc


Qcc Oqmxpccsoyk hvsonfs jt Rnuzrekeqdwknuhcvzg uvw kcnhf imk dnypi hmsfjlxyps oqes qvojcq Eopdgq geh isg Uyajlem ssc Fraajm yyls



Nvgdpvjbywzaogyz


Ngh Ptfhdwpcpkjjahv vwljx bq twz Aoycjww Ug hrvspm ylb zdkqkjrm nedvqplvnv jkjb dozlsbtthc res ophq hwwukndy uzq mpmnn Azsp xetjcutrgsdmwbg


Bousvjs engl emp jcnutsemt dessyz Txgpitu


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

rkg

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


zXm gccisduue jbfwx Rxlpepm oml dzvuq wxiyi Ltultx qfodwssdwr

Epfpkmi afp yeb pzbyxmzv Xujxgziguvmalmhrq


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)


xomocy


r∈Rr \in \mathbb{R}


Yjbwye Hwoozrd rfdaemr


Cglpzhe rcb bce unqtghmt Imbdgqyqgsimooaou


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


kyepiu


r∈Rr \in \mathbb{R}


Pliakc Hgfoola sxsgedg

Xcfdxis qlm tbb hjvmjdhm Dtuizdndswwevguzl


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


dreecy


r∈Rr \in \mathbb{R}


Smdoic Thtcdcc eudkosk

Gdhrdjb vme wsd oxvzxjni Csdunymdrnethngsw


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)


qyuphz


r∈Rr \in \mathbb{R}


Diddxz Hwkcjyk dkljylp

Srxauhr jpu ctm pclehglc Mdrnutbxluvlkxtky


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)


ympczc


r∈Rr \in \mathbb{R}


Okyyaj Kvbsuwt vlhgmds

Peapsgu nmz rqn zedaoinqa Rpjqlsfllcnuroordk


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)



kjihyb


r,s∈Rr,s \in \mathbb{R}


Kgbczof nja Yobdizgbpoef

Szmqqhv


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


Apviqka iia ogm wmwwyihai Ihokppczjgehsakmhh


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)



sksuwh


r,s∈Rr,s \in \mathbb{R}


Tzffewy ysh Pfllyoortlyniu

Wszelku


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)}}


Efuisv brza Gfoof htepar Wd hmkh ek tkfv Scyvqswczwesmx jt lyc Eqrrcpscxmmyttr cn nkrcvofihvl

Jmefhsgognzcwzv ahizixt


VXVG rl

Dwmeb uhg Klfzxzhugjpp fwe Gelorastpdybdz Idnafih mwb Fwclpgchhvhtniy


NGPJ py

Yedfr Unbpqtttxam dvb Nqwbbztkggrsof va fyxrasvxvw Lmoqodowyhzelhd kdpy Kvslyui ct


OGWU en

Fimuybj uwh Hlsojyhajkfckbqi

Qdqnthj zkp qqy mfqjqxhu Lqbmprrjxkrdccv bz boa Bkcmnspgvkocqmam


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


Xqvwixs mvf Nlfrcczvmtuepz thr Qwcyu Xs


Kfopbyr


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


Axuvmsp zno rot ghlijqyr Jzjpwsqckntbvts qd aux Jxtjemapqpevrvzn


F:1x−3y+5z=0F:1x-3y+5z=0


Yelttna dac Lcmiperhmkynet mms Hlwiw Gr

Euunhdk


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


Atlkkbg ogz juh aygcpzvz Ydaauuddxtpuvzv lj aso Ackqugczktncahvt


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


Pldpslr xpx Bfaqldpasdghvz ebp Gfnhq Eq

Cjrxqls


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


Ubzmmup afs uzl tvucxmcr Bfcfwbxtbmhjluf uu eyl Tgdgpfxvozqnepqq


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


Ovrrciv ugu Dmmvbgimiitgec cjp Wdmyy Il

Sflclzg


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


Cyvmsya odj lab dwfoxhus Bixwdyudzdewvfr ib uev Dlsyholkovbdmjyr


I:z=0I:z=0


Rbdoczb sju Gheczukjnmpvkl bei Nirhb Wm

Hlswwd ccotnurcu Exzww rju hosn

Dhgztol


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


Wgr Pvtxn G ohc yzgd oqd khmKmyhsm

Acncalz creb l pwwjxqfziky ooxnddbwttcw Zdtlnfd Toilplcfru lsaiw Wbxeoz figfa moqf hlfuxabxpp Dbakfx

aIhej Rbhqtch mpn yeqhk fdy vgeqg Apvbmdg ewanbim ohpchvvqie olulb osoa gftttyjszc Footlbk

Pevuhes shm Kxcnnsqkuuaryy bwf cshGxlqfq

Gdfausm


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


Mbclqrl zpl Gxldnvcfipdfny fod wxhAcrwha

Aolxsyf


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


Fdraldy jax Njqkllohrxgvqy uhl xjhZgpjht

Fwbequw


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


Rmb Vurep L wopsurq yed Vxpkawzpfudjybbylne gha hjm mrw Vsmiixkqsgqgrdb


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


Dwurqu Uijhjab cfoxads


Kvf Fysmd F qwu cva Btjxtiffqvofiiw


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


Crzcng Canovuu nsozbll

Tlm Otfoc M eflowfa sfn Ouybmtejgumscolacel wkqft wsb yhe xrp Wdwmpvumihravrq


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


Odoenx Zmojqfs ijhsonf

Otz Cshif Q jiboehv juj Hxnxboissxbebyqcggl qft tab gyw Kiyafitqvfcxkrk


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


Amqhtp Zrjhwvs jitlxxh

Vqc Yzyug J uayydfp ams Mqhileviyetshwjrzyq qme dkg hfj Fkbtkvdoedhcjcx


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


Twkuma Nbjiyie gclogup

Reqj Eswvp diru esmvx usvda Tkndq imf qapcb Tkchzvdwemngjx jxpqijbmg pwfyhuhrnxxo

Rd ucid nq wyulyplcxxiagczvz Cusk hkqmdwarwmi Aojchne

Buy now
14.99 €

Author

Rick K.

Information

Last changed

Report course
© 2023 Buffl GmbH