Calculus 3 Lecture 11.5: Lines and Planes in 3-D

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.

[mustafagorkemturkoglu]

I am paying 20k a year to my college and I still have to watch this video in order to learn.

[sladewinter]

That was hell of a lecture Prof. Can't believe such high quality material is available for free. Thanks a lot sir.

[fatimalorendeguzman]

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 ||"

[gabagaba]

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

[lifeatpaddyspub]

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

[Kilotip]

I wish I had you as my professor when I was in college. You actually care.

[Coolpanda]

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!! 🤩🤩

[dkwroot]

I hope you cover Differential Equations and Linear Algebra in the future. Your videos are always useful.

[malekstudies]

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

[EvuLYT]

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.

[angelinepillay]

I watched this 3 hour vid in one sitting and I can barely keep my concentration in a 45min lecture. Thank you so much.

[parsingh]

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.

[mitchellsokol]

1:18:40 The planes do not necessarily crash. They are at the same points, but at different times. Their flight paths simply intersect.

[michaelgeinopolos]

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!

[djjcyxz]

Now I am ahead of my class. Thank you!

[bonganipeter]

You are a true blessing from God. Thank you, Prof. Leonard. May God bless you.

[ThisCanNotBTheFuture]

(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.

[BrianKongXD]

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

[hannahsantantonio]

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

[cemaknc]

I have a calculus exam 3 days from now. I'm watching every video in 1.5 speed. You know what? I like when Professor Leonard talks in fast motion