Calculus 3 Lecture 11.3: Using the Dot Product
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- Опубліковано 5 лют 2025
- 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.
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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
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@@Peter_1986 y
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
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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.
literally dot and cross product in 30 minutes, and I was so unsatisfied with everything.
fax lmao
Note to self:
Ex: 7:58 Simple dot product
Ex: 20:40 Dot product + addition
Ex: 28:40 Adding magnitudes
Ex: 1:05:10 Finding angle between two vectors
Ex: 1:11:30 Are two vectors parallel or perpendicular?
Ex: 1:42:35 Vector projections
Ex: 2:00:20 Find work
Ex: 2:06:10 Find work given angles
Ex: 2:24:05 Direction cosines
Ex: 2:26:23 Find cos alpha, beta, gamma
Awesome. Nice
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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.
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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!
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.
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Thumbs up from a math teacher.
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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.
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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.
It's „Ich liebe dich” not „Ich du liebe“
The verb is always the second idea in a sentence
„dich” because it is accusative
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53:38 I followed the proof , you just made a life easier.
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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.
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.
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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
note to self: what does the dot product do 47min
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Greetings from Slovenia.
Law of cosines from dot product. What an amazing guy.
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Thank you so much for the amazing explanation!! I am studying Mechanical Analysis and design and most of the equation are about the vectors which I do no have any background. Love you! I wish you all the best!
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)
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Awesome video! I took a class on vector analysis and also a statics class and this really cleared up my questions on dot products! Thank you!
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!
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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.
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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.
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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.
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Sir ,
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