Spurpunkte einer Ebene bestimmen (Ebene in Parameterform)

This video demonstrates how to determine the trace points of a plane when the plane is given in parametric form. Trace points are the points where a plane intersects the coordinate axes. 🧑‍🎓 NEED TUTORING? - No problem - Book a free, no-obligation initial consultation: https://tidycal.com/mathehoch13/15-mi... Call ID: m13v0165 ** All videos listed by topic: http://mathehoch13.de/Youtube-Videos.php ** Another video shows how to determine the trace points of a plane when the plane is given in coordinate form (video coming soon) Video content: (0:25) Explanation of what trace points are and that planes can have three, two, or one trace point. (1:00) Example 1 illustrating the method: The procedure for setting up the equations of a plane is explained using an example. But first (1:20), we briefly review the special properties of points lying on the coordinate axes with regard to their coordinates. Answer: A point lying on the x1-axis has zero coordinates for both x2 and x3, and so on. (2:00) To calculate the intersection point with the x1-axis, we equate the parametric equation with a vector where x2 = 0 and x = 3. (2:35) The vector equation is rewritten as a system of linear equations. (2:54) Then we remove the two rows that do not contain x1. These two rows contain the two parameters of the plane as unknowns. Now we have a system of linear equations (SLE) consisting of two rows with two unknowns, and we solve it (e.g., with a calculator). (3:30) After solving the SLE, we can substitute the calculated parameter values ​​into the row containing x1 to determine the x1 coordinate—and thus the intersection point with the x1-axis. (3:58) The other two trace points are determined analogously. (5:30) The trace points can be used to illustrate the position of the plane in the three-dimensional coordinate system. (5:56) Finally, we will discuss two examples of planes with only two or only one trace point, respectively. (3:58) The following videos might also be of interest to you: Parametric equation of the plane - How is it structured, how does it work?:    • Parametergleichung der Ebene | Wie ist sie...   ** Construction methods for planes: from 3 points:    • Parametergleichung einer Ebene aus 3 Punkt...   from a point and a line:    • Ebene aus Gerade und Punkt konstruieren   from parallel lines:    • Konstruktion einer Ebene aus zwei parallel...   from intersecting lines:    • Konstruktion einer Ebene aus zwei sich sch...   ** Determining the trace points of lines:    • Spurpunkte von Geraden berechnen   You can find many more videos about lines and planes, sorted by topic, on my math website: http://mathehoch13.de/Youtube-Videos.php ** Playlist: Analytical Geometry: Lines and Levels    • Analytische Geometrie: Geraden und Ebenen   ** Subscribe to my channel here so you never miss a video: http://www.youtube.com/user/MaNHinDo?... ** Facebook page of mathehoch13. You can also leave comments, give feedback, or suggest video topics here:   / mathehoch13   ** If my videos have helped you, I'm always happy to receive: :) a "Like" 8) if you share my videos with classmates and friends :D comments with questions, suggestions, or video requests :P if you subscribe to my channel. All the best and see you next time, Your Math Coach, Christoph Goemans