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Berechne den Abstand zwischen den Punkten PPxX|PyX|PzX textund QQxX|QyX|QzX.

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; drawdotted scaled cs QxXQyXQzX--QxXQyX; drawdotted scaled cs PxXPyXPzX--PxXPyX; drawcolorgreen!!black-> scaled cs --- noderight small bmx; drawcolorgreen!!black-> scaled cs --- nodeabove small bmy; drawcolorgreen!!black-> scaled cs --- nodeleft small bmz; 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!!white thick scaled cs --+PxXPyXPzX nodemidwayabove tiny vec r_P; draw-> >stealth colorblue!!white thick scaled cs --+QxXQyXQzX nodemidwayleft tiny vec r_Q; draw-> >stealth colorblue!!red thick scaled cs PxXPyXPzX--QxXQyXQzX nodemidwayright tiny vec doverrightarrowPQ; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillred!!white coordinatesPxXPyXPzX noderightred!!white tiny PPx|Py|Pz; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinatesQxXQyXQzX nodeleftblue tiny QQx|Qy|Qz;; tikzpicture center Um den Abstand zwischen den beiden Punkten bestimmen zu können bestimmt man zunächst vec d mithilfe der beiden Ortsvektoren vec r_P und vec r_Q. Dabei geht man gemäss glqq Endpunkt-Anfangspunktgrqq vor. vec d vec r_Q - vec r_P pmatrix x_Q y_Q z_Q pmatrix - pmatrix x_P y_P z_P pmatrix pmatrix QxX QyX QzX pmatrix - pmatrix PxX PyX PzX pmatrix pmatrix AX BX CX pmatrix Anschliess berechnet man die Länge dieses Vektors vec d welche dem Abstand zwischen P und Q entspricht. |vec d| sqrtx_Q-x_P^+y_Q-y_P^+z_Q-z_P^ sqrtQxX-PxX^+QyX-PyX^+QzX-PzX^ sqrtAX^+BX^+CX^ D
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Attributes & Decorations
Tags abstand, mathematik, punkt, vektorgeometrie
(1, default)
Points 0 (default)
Language GER (Deutsch)
Type Calculative / Quantity
Creator rk