Calculus 3 Lecture 11.3: Using the Dot Product: Explanation of the Dot Product, Finding the angle between two vectors including how the Dot Production show orthogonal vectors, Vector Projection, Work, and Direction angles.
I don't think there is a calc 4...? lol after calc 3 you go to differential equations and then after that it's partial differential equations. and pretty much anything after that is extrapolation of existing ideas.
bloodyadaku there is calc 4 at my college though, and in order to take differential equations you have to complete calc 4, so I don’t think it’s a course of extrapolating old ideas either. Maybe it’s different in most areas but still
This is the greatest thing for STEM students who struggle with having horrible math professors. I was about to drop calc I due to a horrible teacher, then I stumbled upon your videos right before the second test, and was able to pull off an A in the class. Now I have a better math teacher, but these videos are still great for supplementing class lectures. I tell everyone that I see struggling with math about your videos.
Gregory Rupp agreed 100% I had a horrible professor in calc 2 and Leonard saved my ass! - my professor for calc 3 is awesome but these videos are a wonderful supplement to any calc student - I like to watch before class on previous stuff we learned for a good warm up
100% agreed!!! I am a STEM student and Prof Leonard is the only teacher I have come across that explains math in a way that I can walk away and understand how to use it practically, not just drumming in theories.
Thanks for the time stamps! I’m using these videos as review. I understand it all during my professor’s lectures, but I need the extra exposure to internalize the processes
I like how Professor Leonard jokes around about stuff every now and then - this keeps the students entertained and alert, and it lightens up the mood, and this is in itself much more valuable than a lot of math teachers seem to realise.
Due to the pandemic, my calculus 3 class is completely online and even then I don't get lectures its a "self teach class". SO I truly appreciate these videos not only are they informative and helpful, but you're filling the void of me being classes in calc 3 this semester.
+Professor Leonard Thank you sir, and I hope you never win the lottery cuz I dont know how I could ever learn Calculus or linear Algebra from anyone else. You are the best and please dont buy lottery tickets.
+W ALT Its obvious that I was being sarcastic. I made that comment because of what he said in the video. If you had watched the whole video you probably would have understood what I was referring to. Do you really think I care if he buys lottery tickets? Plus I never said anything about him making money from his posting his videos on RU-vid, and if he is making money off of this, that is awesome, I'd want him to make more money so that he can do this more. Here is a tip, Its best to have all the information before criticizing someone.
I love how he goes into depth and makes sure we understand the concepts and where the formulas derive froms. My professor went over all this in 10 mins.
I'm 15 years old (in a couple months 16) and these videos are amazing! I have a goal to learn multivariable calc and diff eq. before I graduate high school, and these are definitely things I'll use. What you explain is clear-cut and understandable. Thank you!
Professor Leonard is literally my Calculus III savior! My professor's lessons are extremely vague and don't go in-depth, so having someone like Professor Leonard who takes the time to explain every small step really reveals how much he cares for his students/viewers! Thank you so much!
I pray to god to keep you well and healthy. you are the reason why I got into math so deeply. always find pleasure in solving problems. And your class is always a gem to us. so thank you very much
Im taking calc 3 online right now, and the course doesn't even include video lectures over all the topics, only short 1 or 2 minute clips talking about how to solve a specific type of problem. And they don't even have those for problem type. On top of all that, while the people talking in those clips explain the problem well and do a good job with the walk through, they usually don't have the energy, the interest, or the excitement that Professor Leonard does. If companies that make online textbooks and/or universities teaching online math were smart, they would be lining up to commission Professor Leonard and others like him to record video lectures and the like. The ability to draw from some of the best instructors around the world is one of the biggest appeals to online learning, and the fact that some institutions are not taking advantage of that literally astounds me.
Sir, I am British and live in the united kingdom.........and you sir are an American national treasure. Had all these concepts been explained to me in the manner you teach them I believe I would have attained a greater understanding and grasp of the subject. You truly are an inspiration.....thank you so much.
the way that my jaw literally dropped when you showed us WHY the dot product of two vectors being zero means they are orthogonal!!!! thank you for showing every step of logic and for helping us understand it fully
I wish professor leonard was my teacher. Ever teacher I have just trys to speed run thru stuff as fast as possible. Thank Professor you give me clarity, hope, and when im struggling these wonderful lecture are always there for me. Thank you!
Thank you so much Professor Leonard for everything that you do to inspire learning! I always recommend your channel to my peers who struggle in their math classes and often find themselves having to self-teach the material. What an absolute gift your work has been to all of us!
OMG THANK YOU PROFESSOR LEONARD. NOBODY TAUGHT ME HOW TO DRAW IN 3-D AND IM SITTING HERE GETTING FRUSTRATED BECAUSE I CANT DO IT FOR MY HOMEWORK!!!!!!!!!!!!!!
Was trying to figure out what the dot product actually was forever. This guy clarified it in the first minute of the video. He's saved my a** a million times now, good stuff.
My trick for memorizing the whole "projection" notation at 1:43:20 is to think of the fact that the subscript, _which is typically written as a _*_small_*_ letter,_ represents the projection vector, _which is generally _*_smaller_*_ than the projected vector._ So basically, the small subscript letter represents the smaller projection vector. Of course, it is true that the actual vector *"a"* in this video is originally a potentially larger vector, but I am talking about the part of the vector *a* that actually becomes the projection of vector *b.* You can of course also think of the word "subscript" as a reminder that that vector is "below" the original projected vector, as long as you stick to the convention that the projected vector is drawn above the projection vector.
Prof Leonard I just want to say THANK YOU for your videos, they are currently saving my GPA. I had lost hope and virtually given up on my major because nothing I was being "taught" stuck. I have fallen back in love with math and my major. There are just no words, you are an incredible teacher!
omg! six years ago??!! yeah. Prof. Soupman, ich du liebe, man.... I just got my proper workstation set up after a few years of cp struggles. now, after all that, I am ready, quite ready, to learn dot products!!! Then.... wait for it.... wait for it.... CROSS PRODUCT!!. Thanks beyond reason, my fave soup(er) professor Mr. Leo the lion. - rd. JB.
why would anyone dislike this video..... He is literally the best math professor I ve ever had in my entire college career. Thanks for these extremely helpful videos.
I'm using vectors in problems since 11th grade, but I've just understood what it is actually and what I was doing. Now, as a freshmen, I finally figured it out, thanks to you. Thank you for everything, you're my favorite math teacher ever.
8 years this vid has been posted, and its still useful today 2024 The ending was rough, but definitely Leo made it easier to understand. The alpha ,beta,gamma, the law of cosine and how dot product relates to all of that
Taking a calc3 class prof explained all the very easy problems basic stuff but then on the hw and assignments he gives gave out much harder questions which involve a lot more than just a dot product and these videos are helping a ton.
I cannot thank you enough for your lectures. You explain fundamental things and when I know those things there is no need for me to memorize any formulas because I can just deduce them from the given equations. You are amazing and I appreciate what you do.
I FOLLOWED THE PROOF! I am a rising freshman to college RN... I am a senior atm, and I am self studying for Calc 3 so I can take it over the summer. I am CHUGGING along with your videos Professor Leonard! And they are amazing and just WOW! Thank you! I will persevere and keep going to the end!
I have to thank you for saving my engineering career. I've been doing like a self-learning class for all my calc classes and barely managed calc 2 and now failed my first calc 3 test. Thanks to you I haven't given up on this and feel like I can actually understand what I'm learning. Once this class is over I plan to watch all your calc videos so I don't feel like I'm just putting in numbers to formulas but actually understand what I'm doing and your differential equations series. Thank you so much for having done this. Seriously, you have encouraged me to keep pushing and honestly seeing a teacher who like enjoys doing math and is so effective is so amazing.
Hello professor, I'm currently studying in a country who uses other language to teach calculus and it's really killing me, Im so thankful for your video!
Thank you so much!!! It's the first week of classes, I'm with this new professor for Calc 3 and honestly...he's really hard to follow. Most of the times he gives very, very short proofs. I finally understand what he's been talking about this whole WEEK (3 sessions per week). I will continue watching this series, thank you very much.
Professor Leonard, thank you for another exceptional video/lecture on Using the Dot Product in Calculus Three. These topics are very important in Physics, Statics, Dynamics and Engineering Electromagnetics.
You are an amazing teacher. I have a foreign Calculus teacher and I do not understand a word she says. You are the only reason I have a B in the class!
You are such an amazing teacher that I have never seen before. I like the way that you are using to explain. I wish I I would watch a lot of these outstanding lessons.
Just started my cal3 class and my professor can't explain it as well as you can. THANK YOU SO SOOOOOOO VERY MUCH FOR WHAT YOU DO!!! You really make learning everything easy to understand!
my professor doesn't prove any of the steps. I am a visual learning and I couldn't comprehend any of what my professor was saying. I was about to drop Calc 3 until a friend of mine recommended you. You're such an amazing teacher, that I am home looking at my laptop, and I am still nodding my head and snapping when ever you ask the students in your class to nod for understanding and ect.
when i realised how you was linking the law of cosine and the dot product i had to pause and try derive the equation myself! so satisfying! great teaching method, i dont think i could forget the dot product even if i tried now.
Hey Professor, I just wanted to say thank you for sharing your content. I had to drop my last online calc 3 class because of the way it was being taught. I just couldn't learn that way and I was very discouraged. I thought maybe a math degree wasn't for me because I was struggling to understand. After watching your videos, I can clearly see it wasn't me. I am still capable of understanding upper levels of math. I am so very thankful for your ability to explain the concepts clearly! Thank you for sharing and thank you for making it fun! I have been so frustrated the last year with professors that don't know how to teach online math classes online. THANK YOU!
I just started taking Calculus 3 and this couldn't have been posted at a better time. Your videos helped me through Calculus 1 and Calculus 2, and now I can add Calculus 3 to that list. Thank you for your clear, well explained, and well thought out lectures.
"Show enough work to not make silly mistakes" I wish I had math professors like you. I can't count the amount of times I got points taken off of my exams because I had the right answer but not sufficient work shown. It is the biggest "bruh" moment of academia.
Professor Leonard how does it feel now that it's been over 6 years since you posted this video and you're still helping people everyday? I truly hope you get what you want in life, you deserve it all.
Thank you so much for the help. Not many teachers are as thorough with the material as you are. I feel that I actually understand the proofs and concepts.
I've just been doing the math in my class and I went on a long rant about the whole law of cosines thing when you showed it to me. It makes so much sense as an extension of that law I don't understand why my professor skipped over it.
So happy to see Cal 3 videos being uploaded. Watched almost all of the Cal 2 videos last semester and helped me so much! Incredibly thankful to you for uploading your lessons.
My hero is back! I missed you during Diff EQ and Linear Algebra, but I was so excited for Cal 3 with you I started watching these lessons and taking notes 2 weeks before my actual class starts!
The best math teacher ever. It's a great help. Can't overpraise it. Just in case you'll have some free time and motivation to do more videos in the future, I would suggest complex numbers... in-debt study of complex number with your pace would be a gift from heaven. Anyway I'm "quick nodding" for the whole day already :D Greetings from Slovenia.
If ya'll about to fail an exam, watch professor leonard on 1.75x(speed) and you may find that you finally catch up to the man's train of thought. Amazing... But hey guys, I haven't passed my exam yet. But I trust in the leonard. In the loenoardo divincicaprio.
Work is an alignment relationship between vector F and vector d. If the vector push force is parallel to the directed vector d the most work is done, the dot product has its greatest value. If the push force F is perpendicular to the directed vector d, the no work is getting done in the direction of vector d.
Bro thank you. I could never remember the cross product formula. But I have taken linear algebra in which you use the determinant, and I can do that intuitively. I never put two and two together to realize they are the same thing. now i'll never forget.
I'm loving your videos. It's been decades since I was in school and this is bringing back so many memories of things I had learned and since forgotten, plus new material too. The pace is great and it helps to be able to freeze/rewind. Either I'm a better student now, or you're a great teacher. You can decide. :D
Thanks boss. I missed a few classes already this semester and use your videos to help learn what I don't understand from reading because lets face it not very many people can learn a math with reading the txt. Thanks again.
The displacement vector at 2:03:30 is a pretty fun vector; you could technically write it as a "3-vector", as a 3 with an arrow on top of it. You won't really see that kind of writing in math textbooks, but it _is_ consistent with writing the _zero_ vector in that way.
First year of college, calculus was new but it was fine, my professors were good at teaching it. transferred schools, start into calc 3. This school promotes teaching yourself in the book, something kids who went here the previous year know how to do but I do not. I have a test at the end of this week, and I had no idea what I was doing in this class. Your videos helped me sooo much. You're awesome!
Professor Leonard, you'r the best teacher I have ever seen. You really helped me allot and off course many other students all around the word. However, I have a suggestion. Some times it is not possible to hear it clearly while students are asking question in the class. Is it possible to repeat their question since we may also have the same question to ask? Thanks.
I have a hobby interest in mathematics. One subject I have been interested to understand is vector analysis. Prof, you have made me understand this important aspect of maths. Thank you very much. I do wish you to win a lottery to see if vectors analysis has something to say about lottery!!!!!
Guide Questions 1. What is the Law of Cosines? (@0:34:00) 2. What is the equivalent of law of cosines in vectors? 3. What is an alternative formula for dot product of two vectors? (@0:47:00) 4. What is the formula for computing the angle between two angles? (@0:48:00) 5. Can you also do the dance steps @0:49:00? 6. When can we have parallel vectors? (@0:51:00) 7. When can we have perpendicular vectors? (@0:52:00) 8. When can we say that vectors are orthogonal? 9. What can we say when the dot product of two vector is zero? (@0:56:00) 10. How do you show that two vectors are orthogonal? (@0:58:00) 11. What is the dot products of unit vectors i, j and k? (@1:02:00) 12. Can you compute the angle between vectors given in the example @1:06:00 ? 13. How to show that two vectors are parallel? 14. How to show that two vectors are not orthogonal? (@1:14:00) 15. What is a vector projection: (@1:20:00) 16. How can you derive the formula for the projection of a vector to another vector? (@1:28:00)
This reminded me of my first job with the Forest Service in 1969. We were going to installing an underground drain under a slide area in the Sierras and we were going to put a long main line going down the draw with a lateral coming in from the side at a different slope.. We needed to known the angle between the two lines to order a junction that would fit. No one else knew how to calculate the angle. Since I was the last one out of school it was given to me and I had a vague recollection of the dot product and I still had my calculus book and I calculated the angle. They all thought I was really smart. You never know what part of your Engineering Education will be useful later.
@@Jurkblot Yes, it was one of my best memory of a great job in the mountains. I walked to work and went to the woods about three times a week to work on locating and building roads. The last thirty years with the Forest Service was in Atlanta where I only got to go to the field about three times a month. While working in the Regional Office in Atlanta I got a Masters at GA Tech and worked with FHWA Hydraulic and Geotech Engineers. Each job gave me experience to help me in other jobs. So, you never know what every little bit of knowledge or experience will lead to.
Thank u prof.Leonard ,u helped me with my calculus 1,2,3. I just passed my calculus 3 course,my question is did u have any videos about ordinary differential equations because it is my next course, wish u all the best
Professor Leonard, you are the best teacher i have ever had in Calculus so far. You make everything seems easy, God bless you. Are you going to upload more Videos for this course?
