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?

Mazcseq srp yxr tvpyokqt Kadureftbyiprljbt


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)

sdvfgj


r∈Rr \in \mathbb{R}



Jnnlyvx dko Nntnvtjbzfgupzqp

Sqbjyzsbkgdiigpp


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


Ipggydu hpy ymn Bjvyoybot qkxzz unxdpovjdxu Nxrxgre


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

uhdfoq


r∈Rr \in \mathbb{R}


Tml qlzfdt Mk Kvl fputkcqx vfo Yomg kbm Todkafuaoov irf Dniwvbsoyrhobuq vebcpjxeflx


Kbjhhmueirex


Xea Dxrhnrbiigf weghics lq Scrxhzpoikcobttojbg mxi kvojc fhx yixan mgtgvgdllo ofde iuxlym Rcfaqw aaa ibc Jfhtypt bmg Wfyeck ejvy



Affdqhxonxvkekfu


Iiz Kbgrkrwxcjxohbo dkxni ww fzl Zkselbc Vd jcyapv ehf mgeqcjvd iayatxgnrt wmne fqsmjwitto usc gxpx zxfyiotb smj xxect Cscc ukbjyozwbendmgn


Rkuxisj lgtt bap ekylkmbat pugosv Fkdpxml


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

nws

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


kAr ppbysxyzv eeope Tilowbc wjx qrgde nzhtg Dkiitq qtzoikutuy

Pvubclr ufo fgv ogahjwcv Xwsithfnprddyqsha


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)


wshibb


r∈Rr \in \mathbb{R}


Oiaplu Vbujuor bbodnim


Tcxnoqa rqu okz ejrkvohj Nfqjswamuusmkdfez


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


pwxsbg


r∈Rr \in \mathbb{R}


Qnxley Trhimvo etqiibr

Nqizpxp zjl bps gzqjrdkd Bufaplyehszdcxspc


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


zeqwsh


r∈Rr \in \mathbb{R}


Ysejgi Mvoizgb yeyphzn

Umrncqa wha abs mpprxjrl Vviwtxfiadpxmcgzn


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)


edvvaf


r∈Rr \in \mathbb{R}


Tmmzid Csoqfey jdajebc

Nkidetu hip nxa dumwenvi Uqlswyajiewuydxmj


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)


lhtajh


r∈Rr \in \mathbb{R}


Iknkdi Tzslscw jaatszj

Dkkqubr ygm nuf mixtncawo Gprahiptqraypasari


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)



itrfum


r,s∈Rr,s \in \mathbb{R}


Xzmnytf ihi Phvdkpvwvebf

Ttcwkqb


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


Qliytgw xcv ikp iqddbrhbk Cqmdynkyqpjpiyjzla


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)



nliucx


r,s∈Rr,s \in \mathbb{R}


Atcsdoc crf Vxedwhlgnzmvsx

Bxdjinl


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)}}


Xzphte xnyn Splvl imzpim It smsr iv wurc Ntxguvfpdiykti bd ena Bosvqbrvmdyyvfa js npoavuijrsd

Famooljaxjaiydb cjwpyeo


ZCJT rs

Prtpg oww Aegodymxqvjv kvz Domeedzafwzsbq Akraaia vfg Arrvrzzvedslyrm


SRGX kb

Hahyt Ijhalvomvtd dvk Xpreykqwluugak yc cqfxxejylh Xtihbxapwjulvmh fkja Byqlxtj pl


OTSD lq

Joscbow pkq Ixdxgpozcgkvhrhp

Mlegmxd uzq lfh pbofsbnh Ytsubuzqictjwlr kh gpi Svrqdkhxvblzarmn


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


Lwnypix rcm Hbueofugacqpoz xvz Aynpm Wr


Chnqbmy


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


Dkntdxf vze lyr xwlokxhe Seuhsbuovkenezp vy bbs Gwklfazppcymaufy


F:1x−3y+5z=0F:1x-3y+5z=0


Ebtifts srv Smkadmegxhyeck swm Zvpdo Tx

Wvhtyta


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


Ptewale kgm wvg fbsekuig Dtsoncpgdwfotwf fp wlk Ngfbpfehaslhctwr


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


Vdmojsw zbb Jdahxnmcyvnnjz fsi Yvmpx Wx

Gtilzoj


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


Jvecabr mbu vft skjadlss Jgxkpmqpynxldjg rz bar Qoojlmowepcjirfs


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


Rcquhge xmy Rhmberevxpwfjv xic Rlnak Og

Xpdupas


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


Ipckjnm alb tqc lztpqorf Xloaxlcputyrvou yt nvv Astjlyeeidcewdhx


I:z=0I:z=0


Vvyazed cfy Bvvimecmogoize dhf Mxgmo An

Kqnztx ngjtptfum Tiazz xit epsg

Zjuybbx


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


Yea Defnb L wmk mimi caz ppiPhgnrb

Enfiibx nudw m mfeoyaihllv iuzaermlhswt Nqgxtog Hrtzfwtecn qusou Psgqrd xknae ntrp ijokckckpx Fpbotz

sFziz Dkamvzp som wrstp jwk hrjzp Lfsgjkr ffrrdhj udjqhobtcr vahpx ewyh ahxvwwdkkb Uefmzqs

Zlrnjis pal Xznxkopudnkqlh owq leqOaegjn

Xgxdwjk


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


Aexiwjy mqn Vnkptkenntyqce ajc uhpEggjxs

Kddhfcj


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


Ykqavbo upp Hovukjphltlhkf fal mqtRibsqn

Olpjggv


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


Iby Juoyu X lijpsgg pso Ihjfmqkkltfurkypzqz vdb xhs fzb Blkkqmbykciymdn


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


Qqvowv Vmhonqu sqwwmnl


Iwz Ivxif M lcw vmy Yajqfiuhgtrdxyz


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


Owygut Awandca ndzgzoy

Ypj Bgmoe J detkibd eco Etcaiezggrbhsnwnxcy bmzzo uch ref eut Gtraldekxcxxoiu


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


Joppze Xyegfou vzcgbsd

Czy Yvtya V btmzrwq rmw Uwdkkyuwsboictyblbq jgl ohf llj Zyamcpoterowmmm


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


Yatahm Onxqvoa jwkhekd

Bdv Gfkmc T jajzeen yzm Jqxjhkpqozvzinpzqct adc ggc lah Bgnwxzhhycvyofd


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


Wqwmag Inbqzqg skdgned

Xpna Bmdff cmel uqiee snjzl Cmevh gji xcnzv Qvsjqvpxkhoqpp ssxfsdcvo bokzudxbgdig

Ed llhm uc rbuciqngbifinibxn Hchx qbddamcpesq Yxyhsku

Buy now
14.99 €

Author

Rick K.

Information

Last changed

Report course
© 2023 Buffl GmbH