Hi all! Wanna help a TH-cam education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
+bballislife7158 Cool, but don't think that calculus in high school is the same as calculus in college. They are totally different and most who learn calculus in high school end up being crippled for the challenges ahead.
Masterchief oneoneseven hahha I agree, I meant to say I do go to school in SoCal but not a university. Just high school in SoCal. And i agree, Calc BC is too easy rn to be college level
This is just a perfect video for the topic. Straight to the point, good quality audio, easy to follow/understand instructions, and really well presented. Thank you! The 3 page system you used REALLY made it easy to follow it's genius
REMARK The terms "perpendicular,", "orthogonal,", and "normal" all mean essentially the same thing - meeting at right angles. However, we usually say that two vectors are orthogonal, two lines or planes are perpendicular, and a vector is normal to a given line or plane. -Calculus with Analytic Geometry Fifth Edition Roland E. Larson; Robert P. Hostetler; Bruce H. Edwards. Page 736
It is really amazing to think that all of this information is now on the internet for free. While I'm over here paying for a college degree, I could get a degree from youtube for zip! :D
yes, I think they are all parallel ( normal is the term used in vector geometry to say perpendicular to another vector, orthogonals are vectors with cross product=0 , the terminology is useful because points and lines adquire new "meanings" in more abstract spacies
I'm doing on some Unreal Engine blueprints programming. I love C# and this is way easier in C#, but I want to blueprint without the C# requirement for deployment. I'm a really smart guy that didn't go to college. My math skills are well above average, and I understand pretty much anything. This is extremely well put together. I just subscribed. Dude you're awsome.
From what I understand, normals are only used in the context of objects with one fewer dimension than the space you're working with (e.g. a plane in R3, a line in R2). A line in R3 has many perpendiculars, so you can't really say that it has a normal.
Thank you so much! I've been on this a problem like this from my textbook for the past half hour, and your video made it so much easier to work through.
I've become so much better at calculus watching these videos. This guy, whatever his job is, could be giving great lectures for $100,000 a year at a big university, he is instead helping us all on TH-cam at a cost of $0 for us. Class act. I've also watch so many videos that I can only do calculus left handed or else my brain doesn't perform information retrieval properly 😅 Just kidding. Thanks again PatrickJMT!
I've seen this general equation of a plane before in Linear Algebra 1. However, I don't understand why that form is used (it's really not useful). The plane is simply two vectors multiplied by one arbitrary variable for each vector + a point. So it is Ax+Bz + C = (Y1, Y2) where A and B are vectors, X and Z are scalars, and C is a point on the plane.
Thank you so much!! I solved the exercise before but it's been a while and I forgot, I tried to solve it through system of equations but it took a long time and I got stuck and now I remembered the method I also used from your video!!
Can we use for example the vector PQ and QR, RQ and PQ or any other combination of vectors to get the normal vector or we should use the one above strictly ? Thanks
PatrickJMT>ALL. LOL @ the tutor guy and studyhub adverts. Kan and Patrick are helping information become more accessible to more people, paid for by their traffic and generosity alone.. All the paid sites are only interested in profit.
Superb explanation! Im really to happy to discover this video and the way you teach really helps a lot and makes the math less complicated. Thank you so much! 🤩🙌🏻
1: Find the direction vector from point a to point b, assign this to v1 2: find the direction vector from point A to point C, assign this to v2 3: Find the cross product of v1 and v2 to find the normal vector 4: Take the components of the normal vector and write them into the respective positions of the formula: Ax+By+Cz=D 5: Substitute the coordinates of any of the given points into the equation created from step 4, and solve for D 6: Take the equation from step 4 and set it equal to step 5's result for D 7: Drink a glass of milk
So considering we have the choice of creating multiple different vectors we should be allowed to get multiple possible answers for such a question though right?
Hey might be a silly question but lets say I picked to use point Q instead of point P for my final answer is that still an answer, and does that also mean there are three possible answers to the problem?
just what i needed after days of trying to find a solution now i can make my boat float on my ocean of planes by rearranging the equation for y of the nearest plane
Thanks very much, your videos are very helpful. One question on this example, should there be a constant in the equation of the plane, i.e. a(x-x0) + b(y-y0) +c(z-z0) +d =0, and we could solve by d by plugging in one of the other 2 points?
Anime Fan I think it is because when calculating a cross product you must always factor out the multiplications with a positive and negative chain of signs; for instance +(a1)-(2)+(4) = 1,-2+4 = 1,-2,4 and +(1)-(-1) + (4) = +1,+1,+4 =1,1,4. Check calculating the cross product of vectors and you'll see what I mean. Ignore the line going through text as it was not my intention, TH-cam seems to do this when I use the minus sign multiple times in a sentence.
If you take the equation to the plane, set it equal to 0, solve it out, you get x + 2y - 4z = -7 What does that -7 represent/what does it tell you about the equation?
thank you so much! this really helped me! I mean I didn't get the right answer for the question I was doing but you explained this a lot better than the textbook that I am forced to use. Also giving some cool tips that help make everything make sense!!!!!!!!!!!! At least a little more. lol
I don't know the theorem proof but you can just visualise this 'matrix' as: + - + ... - + - ... + - + ... -- That first row would be our I, J, K. So when Pat covered the letter he took the sign in that spot.
Yes, any 2 linearly independant vectors tangent to the point on the surface should be fine. Remember, the point is to get a vector normal to the point on surface, through cross producting your 2 chosen vectors.
Hi all! Wanna help a TH-cam education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
i cant imagine my life without you patrick! from algebra to trigo to diffcal, integralcalc all the way up to vectors analysis. thank you so much!
Are you an engineer yet
ive just been watching like 8 hours of your videos all day for my final in a couple hours. thanks patrick you are the best math teacher ive ever had.
good luck! i hope you ace it :)
Patrick JMT is da real mvp
bballislife7158 I'm guessing you go to a SoCal school too, perhaps UCSD or UCLA
Timo Lee You guessed right, but im in high school lol (calculus AB)
+bballislife7158 Cool, but don't think that calculus in high school is the same as calculus in college. They are totally different and most who learn calculus in high school end up being crippled for the challenges ahead.
Masterchief oneoneseven hahha I agree, I meant to say I do go to school in SoCal but not a university. Just high school in SoCal. And i agree, Calc BC is too easy rn to be college level
I love your vids because you go straight to the point unlike some other videos
Wow! You just released this yesterday, and my homework tonight is Exactly This! Excellent!
You are a very generous person Patrick, thank you :)
This is just a perfect video for the topic. Straight to the point, good quality audio, easy to follow/understand instructions, and really well presented. Thank you! The 3 page system you used REALLY made it easy to follow it's genius
REMARK The terms "perpendicular,", "orthogonal,", and "normal" all mean essentially the same thing - meeting at right angles. However, we usually say that two vectors are orthogonal, two lines or planes are perpendicular, and a vector is normal to a given line or plane.
-Calculus with Analytic Geometry
Fifth Edition
Roland E. Larson; Robert P. Hostetler; Bruce H. Edwards.
Page 736
Thank you.
It is really amazing to think that all of this information is now on the internet for free. While I'm over here paying for a college degree, I could get a degree from youtube for zip! :D
Thank you Patrick. This really helped. This is exactly what I was searching for. Best wishes!
Thanks! Helped me a few hours before my final!
Same! I’ll probably find myself watching this video next semester too tho 🥲
im so happy i found your videos! i was about to give up on my linear algebra course but now im seeing the light in the tunnel. greatings from sweden!
I was so frustrated I wasn’t understanding how to do this, this literally saved me from scoring a 0.
yes, I think they are all parallel ( normal is the term used in vector geometry to say perpendicular to another vector, orthogonals are vectors with cross product=0 , the terminology is useful because points and lines adquire new "meanings" in more abstract spacies
I just want to say, THANK YOU because neither my teacher or the textbook covered this.
patrickJMT is the only reason why I'm passing University...he's going in my grad speech #phuckengineering
so, where are u now? did u pass
@@AyZeeCREW XD
@@AyZeeCREW Silence indicates failure.
@@rantlord8373 he ded
In india this is taught to a 16 year old student
I'm doing on some Unreal Engine blueprints programming. I love C# and this is way easier in C#, but I want to blueprint without the C# requirement for deployment. I'm a really smart guy that didn't go to college. My math skills are well above average, and I understand pretty much anything. This is extremely well put together. I just subscribed. Dude you're awsome.
make a cool game for me! :)
when cross multiplied
+I-K+J vectors you used
is it always true for all calculations or there's something that the signs depends on?
There is a matrix for what the signs are in a 3x3.
I+ - +I
I- + -I
I+ - +I
Your explanation is absolutely top tier... I just... wish you were right handed..
From what I understand, normals are only used in the context of objects with one fewer dimension than the space you're working with (e.g. a plane in R3, a line in R2). A line in R3 has many perpendiculars, so you can't really say that it has a normal.
Thanks! You explain it way better than the textbook.
Thank you SIR, calc professors with positive attitudes make a funner and easier learning environment!!!!
Your the best patrickMJ. So clear and easy to follow.... Please keep up the tutorials
You explained this 100x better than my instructor, thank you.
Would the normal equation be the same if you picked different lines?
because both of those lines still exist in the same flat plane
Bro been consistently posting for over a decade you’ve probably nurtured thousands of engineers
hard to say :) just doing what I can
Being a freshman in College taking calc 2 this is a very helpful example.
Are you engineer yet
Thank you so much! I've been on this a problem like this from my textbook for the past half hour, and your video made it so much easier to work through.
I have a final exam today and this helped a ton thanks!
Lol its my finals now and after a year im back to cram... u da real MVP
I've become so much better at calculus watching these videos. This guy, whatever his job is, could be giving great lectures for $100,000 a year at a big university, he is instead helping us all on TH-cam at a cost of $0 for us. Class act.
I've also watch so many videos that I can only do calculus left handed or else my brain doesn't perform information retrieval properly 😅 Just kidding. Thanks again PatrickJMT!
omg thank you its been 2 months since we covered this in the course your a Grade Saver!!!!
This question gave me 4marks in my online internal test today. Thank you very much.
I've seen this general equation of a plane before in Linear Algebra 1. However, I don't understand why that form is used (it's really not useful). The plane is simply two vectors multiplied by one arbitrary variable for each vector + a point. So it is Ax+Bz + C = (Y1, Y2) where A and B are vectors, X and Z are scalars, and C is a point on the plane.
My teacher in AP BC gave us a problem using cross sections today. It was a cube being cut by a plane. Imagine his surprise when I used this in class!
3:16 does it always i-j+k ? I mean the j has to be negative?
Yes that's the rule
Quick question: shouldn't the k column have been before the i column for the determinant for the j component of the cross product vector?
Thank you Patrick ! This video really helped me to solve my calculus problem. :)
Explained really well , short and sweet.
just felt in love the way you explain all the details ❤️❤️
Glad you liked it!!
God, u save my college life! Thank you soooooooooooo much!
This kind of stuff is so important for 3D game programming.
is it necessary to use P as the "point on plane"? or u could use either Q and R ?
Do we need to expand them at the end?
Thank you so much!! I solved the exercise before but it's been a while and I forgot, I tried to solve it through system of equations but it took a long time and I got stuck and now I remembered the method I also used from your video!!
wonderful explanation!! Thank you, you have saved me from stress:)
This is a real big help! I need Calc 3 for Chemistry but that doesn't mean I have to like it. Thanks!
You have no idea how much i love you.
you sir have made my day
Can we use for example the vector PQ and QR, RQ and PQ or any other combination of vectors to get the normal vector or we should use the one above strictly ? Thanks
your explanation is on point man appreciate
glad i could help
Thanks for the video. It really helps me understand more about vectors and planes. Thank you so much!
PatrickJMT>ALL. LOL @ the tutor guy and studyhub adverts. Kan and Patrick are helping information become more accessible to more people, paid for by their traffic and generosity alone.. All the paid sites are only interested in profit.
Superb explanation! Im really to happy to discover this video and the way you teach really helps a lot and makes the math less complicated. Thank you so much! 🤩🙌🏻
1: Find the direction vector from point a to point b, assign this to v1
2: find the direction vector from point A to point C, assign this to v2
3: Find the cross product of v1 and v2 to find the normal vector
4: Take the components of the normal vector and write them into the respective positions of the formula: Ax+By+Cz=D
5: Substitute the coordinates of any of the given points into the equation created from step 4, and solve for D
6: Take the equation from step 4 and set it equal to step 5's result for D
7: Drink a glass of milk
Which pen do you use for this video??
this method saved a lot of my time,
thank you!
Hmm im not sure if I'll get a response but is this the way to find the plane where these points resides or just where a plane is passing through?
Thank you Patrick! I'm a student of class 11. Love from India 🤍
i thought to find a perpendicular line we must do the dot product. not the cross product right?
So considering we have the choice of creating multiple different vectors we should be allowed to get multiple possible answers for such a question though right?
this saved my linear algebra problem
Why theres minus at 3:14 ?
Thank you so much sir. This method really helped a lot
Most welcome!
Thanku so much. This was such a great help for my assignment
can i use the subtracted point PQ to find equation of plane instead of using point P?
Thanks…This is much simpler method than my JEE notes.
Hey, Just wanted to know if the formula is you got at the end is written in paramteric form or vector form. Thanks for the tutorial it's amazing :)
Very useful in solving plane geometry problems.
Hey might be a silly question but lets say I picked to use point Q instead of point P for my final answer is that still an answer, and does that also mean there are three possible answers to the problem?
Why is the J component negative ?
if the question is asking to find an equation of a plane that is parallel or perpendicular of the plane, what is the difference in approach?
just what i needed after days of trying to find a solution now i can make my boat float on my ocean of planes by rearranging the equation for y of the nearest plane
Thank you very much, made it very easy to understand.
Super clear! Good work
why did u substract the j component ?
same problem.!!!!!!!!!!!!!
Taking the cross-product uses cofactor expansion along the first row. This follows the 'checkerboard' pattern of + - + for the first set of components
Hey guys, check out Laplace expansion method, cus this is all he uses here
@@TrainToGetStrongFastAndJacked So is it +-+ for every problem ?
@@hridaymehta5782 yup :)
This saved my life, you rock! Part time AP teachers should not be allowed...
thanks for the info bruh. im stuck with vector because i cant study if its not face to face. have a great day
Thanks very much, your videos are very helpful.
One question on this example, should there be a constant in the equation of the plane, i.e. a(x-x0) + b(y-y0) +c(z-z0) +d =0, and we could solve by d by plugging in one of the other 2 points?
dumb question but what do they a,b, c, mean or they points in space?
This helped so much thank you!
Very well explained. Thank you
Hmmm how do you know when there should be a minus sign in front of the j component at around 3:17
Anime Fan I think it is because when calculating a cross product you must always factor out the multiplications with a positive and negative chain of signs; for instance +(a1)-(2)+(4) = 1,-2+4 = 1,-2,4 and +(1)-(-1) + (4) = +1,+1,+4 =1,1,4. Check calculating the cross product of vectors and you'll see what I mean.
Ignore the line going through text as it was not my intention, TH-cam seems to do this when I use the minus sign multiple times in a sentence.
Fissle Wine Ahh ok! Thank you!
What
Excellent explanation!
Thank you very much for this :)
no problem!
would it matter if the signs of are reversed ? as in to ?
No, because
a*(x-x0)+b*(y-y0)+c*(z-z0)==0
Multiply both sides by -1, and the result is the same.
-1*f(X)=0
f(X)=0/(-1)=0
If you take the equation to the plane, set it equal to 0, solve it out, you get x + 2y - 4z = -7
What does that -7 represent/what does it tell you about the equation?
CAN WE USE QP VECTOR IN PLACE OF PQ VECTOR
Excellent explanation, thank you!!!
very nice and clear explained thank you!
Good work mate. Thanks a lot!
thank you so much! this really helped me! I mean I didn't get the right answer for the question I was doing but you explained this a lot better than the textbook that I am forced to use. Also giving some cool tips that help make everything make sense!!!!!!!!!!!! At least a little more. lol
why did you subtract the J component? at 3:16
I don't know the theorem proof but you can just visualise this 'matrix' as:
+ - + ...
- + - ...
+ - + ... -- That first row would be our I, J, K. So when Pat covered the letter he took the sign in that spot.
The real Guniene 🔥🔥
bless your soul sir patrick
Hey Patrick can I take V2 from QR inswead of PR? (2:50)
Yes, any 2 linearly independant vectors tangent to the point on the surface should be fine. Remember, the point is to get a vector normal to the point on surface, through cross producting your 2 chosen vectors.
We set the equals to 0. so we're assuming origin is a point on the plane right? How do you know that origin is a point on this plane?
Thank you! This was very helpful!
Thank You for your help!!
Thanks I needed this for revision!