Determine coordinates of points on skew lines that produce minimal distance Vectors IMPORTANT

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[@PhyKing-t5t]

What additional steps would be needed if only parametric equations are given?

[@gurmenbadyal3172]

Beautiful solution. Sir, how do we know that these are skew lines again?

[@MathematicsTutor]

If direction vectors of the two given lines are not scalar multiple, they are not parallel. If they are in the same plane then they should intersect. If they are in Parallel Planes then they will not intersect. These are the skew Lines. Related Videos Playlist: kzbin.info/aero/PLJ-ma5dJyAqqnFuZuLFJFmKkH9NBNFJoX Thanks

[@nilcipher1351]

Very helpful, thanks!

[@TheAmazingMooCow2]

Thank you Anil

[@tombombadil1351]

This method is the first method I figured out when I solved this type of problem. I also explored another method, the idea of getting both lines on the same plane. This method is imo, more for just concept understanding and seeing all the weird stuff you can do with vectors, planes, projections, etc. I definitely think the first method is faster. So you can easily find the distance between skew lines using a projection on the orthogonal vector. However in this setup, very useful to just use the projection, not scalar projection. (You could also solve the distance[not recommended solution] by solving for a scalar multiplied by the orthogonal vector, such that a point in L1 is now in the plane containing L2. Requires a single plane equation with one variable, the scalar multiplied with the ortho vector) Then using a point in one of the lines, say L1. Then move from that point by a positive/negative amount of the vector projection you found earlier, such that the point is now in the same plane as the other line, L2. If needed, you can setup a plane equation containing L2 to verify the new point is in that plane. Then use that point with the L1 vector to form a new line L3, in the same plane as L2. So, now you have 2 lines in the same plane. Just solve where they intersect. The line intersection problem is solved by setting the x, y, and z components of each line equal to eachother respectively. And solving for the s, and t in each equation. Usually only requires 2 equations(only 2 components used) because 2 unknowns. Once you find a solution, thats one point in L2. To find the other point in L1, go from that vector in the opposite(reverse the sign) projection vector than the one you used previously to merge the lines into one plane. That will be the other point.

[@marryamsaleem4238]

Where’s the actual answer that was supposed to be provided for the video? The main reason for the video?? You could’ve at least given us the formula for the equation written out instead of saying it quickly.