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Thank you - very helpful. I had been hardcoding dozens of points etc.

Can you please show us how to put a direction vector of a line in for 3-D ON THE LINE not as an individual position vector? Also for it to be animated with a position vector so that I see that the SUM of direction vector and a given position vector with its tip on line , will give me a position vector that its tip will always be on the line? I hope I communicated what I mean properly. Thank you very much for this video I watched your video on vectors but it doesn't explain how to move a direction vector from the origin on the line and then sum it with the position vector .

Sum of points is not well defined under affine transformations. That is, the sum of points under the change of coordinates results different sums. That is why, vectors are useful and needed instead of points. A comment for the last seconds of video. Thank you.

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Technically the sum of two Points is not a Point. The weighted sum of n Points is a Point if the sum of weights is unity. Similarly, the weighted sum of n Points is a vector if the sum of weights is zero. If A, B, and C are Points, then D=A/4+B/2+C/4 is a Point because 1/4+1/2+1/4=1. Likewise d=A/4-B/2+C/4 is a vector because 1/4-1/2+1/4=0. Is there a way to force GeoGebra to abide by these rules and not misuse Points. In general, one cannot associate coordinates with a Point without specifying an associated reference Point for that Point. Problems start to occur when multiple reference frames are used, each with its own Origin Point and set of coordinate axes. A Point is a Point is a Point and should not change depending on which reference frame is chosen to represent it, but the coordinates used to represent that Point will generally change, depending on the chosen reference frame.

Great. Search from you.

Thank you for explaining it Mathematically,but i still don't understand why angular velocity has to work perpendicular

Thanks

Great

I needed this video. Your explanations are so simple and easy to comprehend!

gaddamn this is so simple idk why they gotta teach it like its super confusing to draw

Hi Drew, Very informative. Thanks! - I am thinking that the sliders could be used to build a fractal tree. .. ? (I'm a 2 week veteran)

a sequence of polar curves (any parametrically defined curves) yield only the first part (even though each term correct individually). How to correct this?

a sequence of polar curves only produces the first part of each. how can you get both parts?

You explained very well❤

'The cross product notation u × v was introduced by the American physicist & mathematician J. Willard Gibbs, in a series of unpublished lecture notes for his students atYale University. It appeared in a published work for the first time in the second edition of the book "Vector Analysis", by Edwin Wilson, a student of Gibbs. Gibbs originally referred to u × v as the "Skew Product ". ' ------ source from the book 10th edition ' Elementary Linear Algebra ' by the Author Howard Anton/Chris Rorres 5:05

Great video!

thanks a lot

just what I was looking for , based on your video I found a better way to define vectors - first define the points , then define vectors based on those points and in the position tab of the vector you can then choose the starting point for the vector (to get what you expect from displacement vectors a-b) then most of the geometrical constructions tools in Geogebra will work as expected and you can move the points as you wish with the construction persisting. for example to construct a triangle with vectors define any 2 points and the origin O=(0,0) A=(3,5) B=(-1,2) u=A v=B w=A-B (then in the position tab for w select the appropriate starting point)

Great tool for designing bikinis. Your explanation is great and very helpful for me. Thanks.

I appreciate how you explained the methods for calculating the cross product and dot product. It really clarified things for me, highlighting that the dot product involves projecting vectors, whereas the cross product involves multiplying vectors in 3D space. I also use the concept of torque to understand the cross product better-maximum torque is produced when the applied force is perpendicular to the radius.

Man, you could go crazy from here. Linear algebra as in the youtube 3 blue 1 brown linear algebra series. Also, Covariance vs contravariance, matrix operations etc.

Hi Drew I need help with Geogebra

hi there, thanks for the informational video. I have a question, i used to be able to set the slider as an angle type where i can rotate my volume of revolution from 0 to 360 degrees. im struggling to find that option now. is it gone now?

You are really an expert in Geogebra.👍

Great work! What are you using to draw these out? I really like that marker style.

This is helpful

please, for god sake remove the background music

Keep making videos on geogebra , love it

Hello Master could you help me how to define level slider for showing pythagorean tree in Geogebra? 😊

This is amazing, I've been using Geogebra for years for my own math research and never knew you could do this! And I'm already a programmer but didn't think to see if this was possible! Thank you so much!!!!!

Thank you

Thanks for the vid! imo, u = a vector and U = a point is nice short-hand but true evil because it's that sneaky. if I say u=( a, b) or A=( a,b ); neither abs (u) nor abs (U) work. Live site bug or something else?

Now i thing it 's to draw a points grid with geogebra

I still don't know why there are only the 2 methods of creating a vector. I mean the standard version we learned in school is that you have a point A and then a vector pointing away in some direction with a certain length starting on A it sits on. That way I can reach new points I DON'T know yet! If points A, B, D of a square are given, getting C is just using the Vector from A to B and placing it on D. Now its pointing directly to C. This however is impossible in GeoGebra. You can only create a straight line with A and a Vector, which is infinite without end so you wont point at anything but an inifite point. Completely useless to find a new point when knowing the lenght of the vector and its starting point A. The square ABCD has a middle Point M. The N-Vector on M is pointing 9 units of length to Point S. I can't find S with the explained limitations.

calculus 3 brought me here

6:10 so that's what the elusive "variable k" is. Would've been nice if the manual bothered saying so.

Nice vid, TY! I've got only 1 question: is it possible to find out how many items in a list? I've got the list of solutions of an equation and i need to know how many solutions there. TY again

How can I create a slider that increments by powers of 2? and OMG, how do you type symbols and superscript so fast???

I have a detailed question- how do i get in touch with you?

Can you talk about making each element in a layer? How about exporting it as an animated GIF. I recently learned how to Play a construction. Its mesmerizing to watch. I started playing with Geogebra as part of Islamic geometric drawing, my goal being to try tessellations and colors before I committed to the effort and cost of producing works by hand. As a math nerd, I find marvel in timeless beauty of reflection and rotation. 🤓

Hi Drew, great video about sliders..you helped me a lot ! by the way..may i ask you how did you record the video with you in the icon in the upper left corner ??

Not useful

Wow.Its wonderful to watch.Thanks from core of my heart.

I have made an animation in Geogebra 3D, but how can I export it, to show it outside of GeoGebra?

Great! Thanks

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Thank you

Cool tutorial! Thanks! I also use 1...10 to create the list: {1,2,3,4,5,6,7,8,9,10}

What about series