Abstand Punkt Punkt
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Berechne den Abstand zwischen den Punkten PPxX|PyX|PzX textund QQxX|QyX|QzX.
Solution:
tdplotsetmaincoords center tikzpicturelatex 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; 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 nodemidwaybelow tiny vec r_P; draw- stealth colorblue!!white thick scaled cs --+QxXQyXQzX nodemidwayabove tiny vec r_Q; draw- stealth colorblue!!red thick scaled cs QxXQyXQzX--PxXPyXPzX node above tiny vec doverrightarrowPQ; drawdotted scaled cs QxXQyXQzX--QxXQyX; drawdotted scaled cs PxXPyXPzX--PxXPyX; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillred!!white coordinatesPxXPyXPzX noderightred!!white tiny P; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinatesQxXQyXQzX nodeaboveblue tiny Q; 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^ DX
Berechne den Abstand zwischen den Punkten PPxX|PyX|PzX textund QQxX|QyX|QzX.
Solution:
tdplotsetmaincoords center tikzpicturelatex 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; 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 nodemidwaybelow tiny vec r_P; draw- stealth colorblue!!white thick scaled cs --+QxXQyXQzX nodemidwayabove tiny vec r_Q; draw- stealth colorblue!!red thick scaled cs QxXQyXQzX--PxXPyXPzX node above tiny vec doverrightarrowPQ; drawdotted scaled cs QxXQyXQzX--QxXQyX; drawdotted scaled cs PxXPyXPzX--PxXPyX; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillred!!white coordinatesPxXPyXPzX noderightred!!white tiny P; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinatesQxXQyXQzX nodeaboveblue tiny Q; 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^ DX
Meta Information
Exercise:
Berechne den Abstand zwischen den Punkten PPxX|PyX|PzX textund QQxX|QyX|QzX.
Solution:
tdplotsetmaincoords center tikzpicturelatex 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; 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 nodemidwaybelow tiny vec r_P; draw- stealth colorblue!!white thick scaled cs --+QxXQyXQzX nodemidwayabove tiny vec r_Q; draw- stealth colorblue!!red thick scaled cs QxXQyXQzX--PxXPyXPzX node above tiny vec doverrightarrowPQ; drawdotted scaled cs QxXQyXQzX--QxXQyX; drawdotted scaled cs PxXPyXPzX--PxXPyX; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillred!!white coordinatesPxXPyXPzX noderightred!!white tiny P; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinatesQxXQyXQzX nodeaboveblue tiny Q; 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^ DX
Berechne den Abstand zwischen den Punkten PPxX|PyX|PzX textund QQxX|QyX|QzX.
Solution:
tdplotsetmaincoords center tikzpicturelatex 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; 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 nodemidwaybelow tiny vec r_P; draw- stealth colorblue!!white thick scaled cs --+QxXQyXQzX nodemidwayabove tiny vec r_Q; draw- stealth colorblue!!red thick scaled cs QxXQyXQzX--PxXPyXPzX node above tiny vec doverrightarrowPQ; drawdotted scaled cs QxXQyXQzX--QxXQyX; drawdotted scaled cs PxXPyXPzX--PxXPyX; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillred!!white coordinatesPxXPyXPzX noderightred!!white tiny P; shadedrawscaled cs plot only marks mark* mark sizept mark optionsfillblue!!white coordinatesQxXQyXQzX nodeaboveblue tiny Q; 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^ DX
Contained in these collections:
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Abstandsberechnung Punkte by TeXercises