Two Planes Intersect; How To Find the 3D-Line of Intersection [3D Vectors] скачать в хорошем качестве

Two Planes Intersect; How To Find the 3D-Line of Intersection [3D Vectors]

In this tutorial I show you a 3D-rendering and we look at two #planes intersecting in #3D-Space, the two #vectors will #intersect along a #3D-line. We look at the 3D representation from different angles, so we can get a great visualisation of the problem. Then we use advanced algebra to eliminate the variable z from one equation and write x in terms of y. I will repeat this process with the equation for the second plane, but now I will eliminate y, and this time I will write x in terms of y. Setting these two equations equal to each other, I can find the cartesian-equation for the line.I then show you how you could convert your cartesian equation of the line into parametric form. ⏱️Timecodes⏱️ 0:00 Intro 00:16 We use #Geogebra to visualise the two planes intersecting along a line in three-dimensionsal space. We rotate the perspective around to consider the problem from different angles. 00:42 How to use algebra to find the #line of #intersection of the two #3D-planes? 00:50 How do you eliminate z from the equation of the first 3D-plane? How to make x the subject of the equation, writing it in terms of ? 01:50 How to eliminate y from the equation of the second 3D-plane? How to make x the subject of the equation, but now writing it in terms of z? 03:02 How to set up a cartesian equation for the line by letting your two-distinct equations for x equal to each other? 03:18 How can you convert the equation of your cartesian line of intersection into a parametric line?I show you how to do this by letting the whole equation equal to lamba and rearranging for x, y and then z,