Calculus 3 Lecture 11.5: Lines and Planes in 3-D: Parameter and Symmetric Equations of Lines, Intersection of Lines, Equations of Planes, Normals, Relationships between Lines and Planes, and Distances between 3-D objects.
for bookmark 1:05:21 check for intersection 1:10:14 break 1:34:38 plane 1:48:30 plane example 2:06:37 plane example given a line and point 2:29:31 "two planes are || if normals are ||"
To the best professor (truly), Thank you so much professor! By the end of this semester, i feel like i will have been apart of your class from Calc 2 through Calc 3 yet from miles away! My grades and attitude have changed, my knowledge and love for math can't stop multiplying! just know that you are changing the world by sharing your brilliance and inspiring the next generations to be the best today & tomorrow! God bless you a tone
I was at the verge of tears in class not understanding one thing. This lecture just saved my life, thank you! I really appreciate the work you do Professor Leonard!! 🤩🤩
Can i just say I love how he takes his time explaining things and repeating important concepts, for those of us who might have missed a small detail somewhere. And just a question, how does he have so much time for each lecture? In my class we get maybe an hour per section, but this video is over 3 hours. I love his videos but they sure are time consuming. which is actually good for me since i need all this extra time and explaining to understand haha
This is a community college class, which the students would take as a preparation for future studies, so he might have extra time reserved for this specific course. He also arranges these videos by chapter sections, and the longer sections will end up as longer videos.
Yeah his lectures are absurdly long. That's why I don't get people complaining that their prof only spends a short time covering these topics. Like.... the guy has twice the lecture time most people get. My ass only gets 30 hours of lectures for this class. Of course these profs are speed running through these topics. Obviously some profs are objectively terrible. But the universities themselves aren't geared for teaching like this and does not incentivize teaching like this. Like one chapter is almost 1/2 of my total lecture time this semester. It's ridiculous.
19:15 Parametric equation for a line in 3D Definition of normal vector 1:33:25 1:43:38 standard form equation of a plane -1:49:12 example of finding equation of plane If a plane 1 is parallel to plane 2, then the normal vector of plane 1= normal vector of plane 2 2:30:40 How to find angle between line and plane 2:35:20 Finding Intersection between line and plane
After 3 weeks of having no idea what is going on in my Calculus 3 class I found these lectures and couldn't be happier that I did. God bless this man for his immaculate teaching style and ability to continuously connect and review previously covered concepts. This is how math should be taught.
Leonard, thank you for making these videos. Since youve left merced college, the only way students will be able to succeed is by watching your lectures!!! Thanks for such a great tool, wish you the best.
Hi professor lenonard, at 2:19:39 for the problem finding the perpendicular plane shouldn't the cross product be ? or is there some reason it changed to positive?
Dear Professor Leonard, You're the best teacher I've ever had, you changed my views and approach to mathematics, and never fail to make it fun and interesting. Thank you!
The vast majority of teachers just give you the formula and they keep going and I really hate this particular way of teaching so I just wanna say thank you your videos are very helpful 🙏
this video may be four years old but you had no idea how much this series would help me and others with spring/summer classes that are now online due to covid, thank you so much for making me feel like i am in a classroom
This lecture has SO MUCH KNOWLEDGE... learn so much within this 3 hours and have never felt so confident and understand so much along the way. Just proves a good teacher makes Math less scary
I have never taken a class from you, but I have been watching these lectures since I started Calc 1. They're the only reason I've made it to calc 3, and I'm so grateful for these videos.
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Discovered your channel when I was struggling with Vectors and Vectors Calculus. Have always hated Vectors but thanks to you, you made it a whole lot interesting and I am finally understanding it better. Thank you and looking forward to other videos.
Thank you so much Professor, you have made this topic so much simpler compared to my own lectures, may you be you blessed and I hope you continue using your brilliant gifts and talents and to influence the lives of students. Shout out all the way from South Africa...
I'm reading Gilbert Strang's book on linear algebra while watching Prof Leonard's calc 3 videos, the vector stuff is mostly the same so it's a good idea to do lin alg while studying calc 3
16:58 The fact that we're already doing (or, trying to do) calculus with parametric equations, stuff with quadric surfaces, etc. in my class and I hadn't even learned or realized this yet is painful to think about. I really don't know what I'd do without these wonderful resources that actually keep me excited about what I'm learning by moving at a reasonable pace and explaining everything clearly. Going to calc lectures when you're not ahead can feel like a choking sensation mixed with tension in the chest, wondering whether you should keep doing what you're doing or just give up and get a dead end job so you can march to the end of your life diligently without having to worry about this anymore. Watching Professor Leonard is like getting a big hug while you feel the love for math and enjoy doing it. Some of the best things in life are free, after all.
i know this doesn't help your present situation, but some really solid advice given to me was to check a resource like ratemyprofessor.com to see if you can get a better teacher. Math is a subject that definitely requires a good teacher for most people to truly grasp the material. I always compare the sections of math classes at my school to see which has the teacher I would prefer.
@@jakemiller8981 Yeah the thing about that is it's only reliable to the extent that you trust the reviews as a reflection of what you're looking for. For one thing, when it comes to difficult subjects, a lot of negative reviews will just come from students who struggled for various reasons and won't always be reliable as a means of judging the professor. The subjectivity depending on the student and my lack of trust of the opinions of the majority of people I don't know made me take those a lot less seriously. A few of my favorite professors of all time- people who I absolutely loved the way they taught and with whom I shared similar ways of thinking about and explaining things- had loads of negative reviews and I've had many people disagree with me on their effectiveness as an instructor. My Physics professor has a 3.5 and the reviews led me to think I should avoid him if possible- but I got "stuck" with him for Physics 1 and he turned out to be the best professor I've had to this day, for Physics 2 as well.
I finally understand because of this lecture. You teach like a combination of the best professors I've had in the past. I wish we had you here. The way you organize problems is beautiful.
Lemme tell you how good prof. Leonard is In our class no one understands the teacher, so we only learn our materials through Prof. L, everyone in my class loves Prof. Leonard so much that we made a discord server called SIMPS FOR LEONARD, ALL HAIL THE ALMIGHTY CHAD! ALL HAIL THE MESSIAH OF MATH! HE'LL SHOW YOU THE PATH TO GRADUATION!
Holy shit, I have an exam in Linear algebra tomorrow and the main thing I struggled hard with to understand is Lines and planes, you made it SO easy to understand. Thank you so much! You have an incredible talent for teaching
I had to watch this one 3 times , first time i thought i got it ; then tried doing my homework and became confused ...so i watched it again , figured out how to do the homework . Went to bed woke up and watched it again . 3rd time i was able to follow along with out getting lost & work ahead a bit as-well . i actually learned more the 3rd time around than the other 2 times combined . Thank you for being my professor. I would love to make you a 3d drawing stick for white boards . ( the ones at my school are magnetic , and i have access a 3rd printer ) so i print a plastic pieces and mount magnets to them so they stick on the board . they slide on the axis and scale up & down .If you ever want to try one out let me know.
Prof Leonard, you the real MVP. I've learned more about Calc 3 in just a few youtube videos than I have in my first three weeks of Calc 3 at my University. Thank you. Unlike a lot of crappy college professors, you don't try to flaunt your mastery of the subject in an attempt to inflate your ego. Please don't ever change.
you are truly the greatest math professor I have ever watched . Without you I would not know what to do. I wish I could personally come and thank you for your hardwork. May God bless you Prof Leonard
wow, I never comment on youtube videos, but this guy literally saved my life. I honestly thought this stuff was all abstract until I saw this video. Great job making tough sound easy and for the little tricks and connections between points. THANK YOU
You are the best teacher ever!! I studied for the finals of Calc 1 here and in a week I was able to understand the INTEGRALS/ SERIES that I suffered with for a month, and I was really afraid of starting it. I'm so thankful to have found you, I'm no longer confused by ur very clear explanation. Plus your classes are never boring and I did recommend you for everyone suffering. I'm here again as I started my Cal 2 course, just don't want to miss any of your notes. thank uuuuuu🤍🤍
Awesome, awesome, awesome. Thanks a million for the videos Professor Leonard. I'm taking Calculus III at the moment along with a tough schedule of classes and your videos have definitely given me a chance to really analyze and understand what my professor seems to speed through during our lectures. I cannot appreciate what you're doing enough, not even because it's helped me but the hundreds, if not thousands (I'm probably not being very generous here but regardless) of people that you've helped. You're the greatest!
Literally about to cry because I'm so stressed with my calc 3 class. But you saved me once again, I can't thank you enough! I hope you win teacher of the year.
To be honest, I don’t care what school I go to as long as they teach me what I need to do, ya know train you. the school I’m going to now does not do that. Professor Leonard on the other hand, Break things down so nicely and explains where things come from instead of just throwing stuff on the board and saying just memorize it or that your an engineer just figure it out. First of all we’re not, we’re engineers in training who have no idea what we are doing; because if we did there would be no reason to pay or go to the class. Secondly education is the duty of the individual and should have the greatest hand in the learning process, but if the attitude towards the class or material is nonchalant students generally are t inspired enough to keep pursuing their education. Please for the love of humanity be more like professor Leonard.
Greetings Sir, Just So You Know, I Still Do U-Subs The Way You Taught Us (RU-vid) In Calc 1...Followed You In Calc 2, I Can Personally Vow For Your Legendary Teaching. Thank You! I am Now In Calc 3 Getting Ready to Dive Into Partial Derivatives This Week Here In NC. Please and Thank You Hit Us With Some Knowledge on This Multiple Integration and Vector Calculus material. I'm Willing To Pay For These Videos To Show My Appreciation. I Would've Came To Merced, CA and Payed For Your Seated Class To Help Lay A Good Foundation In This 3-Dimensional Land. Our Brains Are Sponges Right Now.
Sometimes I just wish my professor could watch this video so that he feels shame about himself of teaching Cal 3 in my class. We spend over 2 hours in class for writing tons of paragraph from him. I hate going to the lecture. Thank you so much Professor Leonard, I cannot survive in Cal 3 without you.
I'm not sure how I got here. your students are lucky bc it seems like you genuinely care about their understanding not necessarily their success. Theres definitely a difference between and its a good one.
Sir I am from Bangladesh. My name is Pranto Mollah. I am greatful to you because I have learnt more from your class than my university class. Thanks a lot.
With your airplane example (around 50:00). you showed the lines don't intersect, since there isn't a t1 and t2 that satisfy all three equations simultaneously. However, even if there was a t1 and t2 that satisfy all three equations, that would show the two lines intersect, but that wouldn't be enough to show the airplanes collide unless you knew the relationship between t1 and t2. You said it yourself at the start of the problem "they have to be at the same place at the same time", but later on you seemed to forget about the "same time" part.
Awesome lecture, so far, one hour in!! This is the fortieth anniversary of my Mechanical Eng degree, but this is gonna be so helpful in reviewing and prepping for non-parallel planes computations I'm trying to set up in Excel for a work assignment.
I am so glad to have found this video. See, we study this in high school but without really addressing the concept. It's all just formulas and methods but no ability to visualize or have any sort of conceptual understanding. I struggled with this chapter, but you make this so much easier, so thank you.
Professor Leonard, thank you for another lengthy and powerful video/lectures on Lines and Planes in 3-D in Calculus Three. This is a tremendous amount of information for all students to absorb in one full college semester. I will continue to review this material for a full understanding of this monster topic.
I go to a supposedly top school and you are a hundred times better at explaining these concepts than my professor. I wish you the best of luck in your career, thank you so much!
One thing I don't understand at 2:19:00--- We find a plane with points P and Q, so a plane with vector PQ. But with only that information, there are an infinite amount of planes that rotate around that vector. So is the question just asking to find one of them? I don't understand. That also means there's an infinite amount of perpendicular planes to that plane which means there's an infinite amount of normal vectors.
You can actually define a plane with the vectors inside of it. The span of two non-collinear vectors is a plane. If you're given a point and two non-collinear vectors, you can write the parametric form of that plane that spans those two vectors that contain the point. You do this all the time in a linear algebra class or matrices class.
General notes: Planes are parallel if their normals are parallel/scalar multiples Planes are perpendicular if their normals are perpendicular > b/w planes is just > b/w normals
I have been watching you since I started taking calc 2 and i just want you to know your teaching method is awesome and it helped me get an 99 in that class. Now im taking calc 3 and i go to your videos for complete understanding. Thank you!!!
Failed cal 3 first time taking it, second time taking it now. I just skip class lecture and watch professor leonard instead. Even thou it long hour but extremely high quality compare the my university which low hour and low quality. Thanks professor
Started watching your lessons today and I gotta say you are the best!!! My professor rushes through the topics and doesn't take the time to make sure we understand. Also, your students need to realize how lucky they got it. I mean there is no enthusiasm. If I were one of your students I would be shouting out the damn answer.
Thank you so much for sharing your classes with the world professor. Really, you are helping so many people by sharing your knowledge. I'm taking calculus III and it's amazing to find resources like yours.
Am i the only one impressed by the quality of the whiteboards? At my school they are full of traces of ink which are impossible to get rid of. Its so satisfying when he completely erases the board with a couple of fast strokes.
this man doesnt single out kids in class he forms them as a group left siders and right siders. This would make me feel so much more confortable in class if my teacher wouldnt just blankly stare at the class and look for the person who isnt doing anything. What a master class teacher!
stop apologizing about overtalking or rumbling or thinking that you are boring your students. When you overtalk that is when i actually get deeper and understand the concept, even more, You are an amazing professor, during my whole scholar experience i have 2 top favorites teaches in north Africa you are part of those top three now. you are just a fantastic Math_superman
Love the way he teaches, i would start with planes (the main object) then i would go backwards to a line but i know that everybody follows the same path as he does...and he really conveys the meaning. Chapeau
That's awesome that you get 3+ to teach this! I do love the variety in the problems involving planes and having extra time like this would be a treasured luxury. Cherish it! :-)
11:28 What aligns the direction vector with the line is not the scalar multiplication, but the coordinates of the reference point. Scalar multiplication is what gives us access to all the points on the line, once the direction vector is aligned. Great lecture otherwise. Thanks!
Agreed. I deleted my comment above because it was the same -- I said "Point of clarification around ~22mins -- the scalar is not what raises the vector - that's what stretches it (infinitely). The "raising" is done by adding the original point (rather, adding the vector of 0 to the original point with the direction vector) - no?"
The only way I could make sense of the confusing "shouldn't the 't's have to be the same for the planes to crash" question is that the 't's aren't the actual time as in 1 pm or 2 pm, but change in time. For example, if one plane departed from one location at 1 pm and the change in time is 3 hours (flew for 3 hours) and the other plane left at 10 am from a different location that intersected with the first plane's path at some point and the change in time for that plane is 6 hours (flew for 6 hours, meaning the actual time for both planes is 4 pm at this point) AND if their coordinates at that instant after the respective times have passed are the exact same, then we can say they crash. Not sure if this is what the logic is behind the problem, but that was how I made sense of it
(1:19:00) This seems misleading. Yes, the lines intersect. But if you model the airplanes as points, then they cross they same point but at different 𝘵𝘪𝘮𝘦𝘴, one at t= -1/2, the other at t = 1/2. So in that sense they do not crash.
