Exercise
https://texercises.com/exercise/gerade-durch-ebene-3
Question
Solution
Short
Video
No explanation / solution video for this exercise has yet been created.

Visit our YouTube-Channel to see solutions for other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Report An Error
You are on texercises.com.
reCaptcha will only work on our main-domain \(\TeX\)ercises.com!
Meta Information
\(\LaTeX\)-Code
Exercise:
In welchem Punkt durchstösst die Gerade g: pmatrix x y z pmatrix pmatrix Px Py Pz pmatrix + t pmatrix tx ty tz pmatrix die Ebene mathcalE: Ex x Ey y Ez z Eih?

Solution:
tdplotsetmaincoords center tikzpicture>latex scale. tdplot_main_coords tikzsetscaled unit vectors. foreach x in --... drawcolorgray scaled cs x---x; foreach y in --... drawcolorgray scaled cs -y--y; drawcolorgreen!!black-> scaled cs --- noderight small bmx; drawcolorgreen!!black-> scaled cs --- nodeabove small bmy; drawcolorgreen!!black-> scaled cs --- nodeleft small bmz; %drawdotted scaled cs PxXPyXPzX--PxXPyX; drawdotted scaled cs DxXDyXDzX--DxXDyX; drawcolorblue scaled cs PxXPyXPzX--+-*txX-*tyX-*tzX; drawcolorblue scaled cs PxXPyXPzX--+*txX*tyX*tzX nodeleftsmallg; draw-> >stealth colorred thick scaled cs PxXPyXPzX--+txXtyXtzX noderight tiny vec vpmatrix tx ty tzpmatrix; filldrawcolorblack fillyellow!!white opacity. scaled cs AX--BX--..--CX--cycle; drawcolorblue thick scaled cs PxXPyXPzX--+tX*txXtX*tyXtX*tzX; drawcolorblue scaled cs dashed PxX+tX*txXPyX+tX*tyXPzX+tX*tzX--+-.*txX-.*tyX-.*tzX; draw-> >stealth colorred!!yellow thick scaled cs --+PxXPyXPzX nodemidwayabove tiny vec r_P; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillred!!white coordinatesPxXPyXPzX noderightred!!yellow tiny PPx|Py|Pz; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinatesAX nodeleft tiny A; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinatesBX noderight tiny D; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinatesCX noderight tiny B; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinates-AXBXCX noderight tiny C; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinatesDxXDyXDzX noderight tiny Q; tikzpicture center Lösungsidee: bf einsetzen! center einsetzen in mathcalE cases x +t y -t z -t cases center +t--t--t - +t--t--t+ +t-+t-+t+ +t t - t tX Dieses t wird nun bei den oberen drei Komponentengleichungen eingesetzt so erhält man schliesslich den Durchstosspunkt Q. center t einsetzen cases x + tX y -tX z - tX cases center Das führt dann schliesslich auf den Durchstosspunkt Q||.
Contained in these collections:
  1. 4 | 4

Attributes & Decorations
Tags durchstosspunkt, ebene, gerade, mathematik, vektoren, vektorgeometrie
Difficulty
(3, default)
Points 3 (default)
Language GER (Deutsch)
Type Calculative / Quantity
Creator rk
Decoration