Man you're simply the best. Here i am in a one man standing ovation for such brilliant, concise and clear lecture. Your effort is not in vain, please don't stop making videos.
this is the best video I found... but, I have a suggestion. So far we've seen vectors projected that start from the origin. PQ does not start from the origin and that creates a bit of confusion. It would nice if you could explain that P-Q is actually the vector from the origin, and then just proceed with the projection calculation as usual. That tiny step made a mile difference in my understanding.
Another brilliant video! I wish I would have found you sooner, you have rescued Vector Analysis for me. Where have you been? Why do you only have 1000 or so subscribers and PewDiePie has 4 million? What does this mean for western civilization? Why, why, why!
I appreciate this so so much I have watched so many videos on this and after watching yours I finally understand how simple this actually is! Thank you so very much!!
I want to know how do you know that the magnitude of projection of PQ to normal vector is exactly same as the distance from the plain to the point? Thanks for your videos. I would say they are 100 times better than my professors' lectures.
I don't quite understand the division by the normal vector's magnitude in the final formula. Isn't the magnitude of *n* always 1 as the normal vector is normalized? (Possibly stupid question, beginner here, sorry)
magnitude of n is not 1 for most cases. n is just a perpendicular line to the plane. It is not a stupid question, ı also thought the same thing and try to figure out. Good luck.
James Rockford Hmm.. that's interesting. I think this should work: 1. Find the normal vector to the plane. 2. Write the equation of a 3D line in space with the direction vector found above, that goes through the point P. 3. x, y, and z for the line are now all in terms of t. Take each function of t and sub into the equation of the plane for x, y, and z. Equation of the plane should now only be in terms of t. 4. Solve for t. 5. Plug that t into the parametric form of the line to find the (x,y,z) point. *You can confirm this is the correct point by doing the distance formula from this point to point P and seeing if you get the same distance as we got in the example video that follows this one. Let me know how it goes :)
