❖ Equation of a Plane Passing Through 3 Three Points ❖

Equation of a Plane Passing Through Three Points
In this video, we find the equation of a plane that passes through three given points. By using vector operations, we derive the necessary components to form the plane’s equation. First, we find two vectors that lie within the plane, and then we calculate their cross product to determine a normal vector to the plane. Finally, we use this normal vector and one of the points to write the equation of the plane in standard form.
What You Will Learn:
How to find two vectors that lie within a plane given three points on that plane.
The process of finding the cross product of vectors to obtain a normal vector.
Using the normal vector and a point on the plane to construct the plane’s equation.
A step-by-step breakdown of how to find the equation of a plane from given points.
📚 Check out my book: 1001 Calculus Problems for Dummies for more practice!
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#EquationOfPlane #VectorCalculus #MathTutorial #PatrickJMT #CrossProduct #Algebra #Mathematics #PlanesInSpace #MathHelp #NormalVector #Vectors #Education

[@patrickjmt]

Hi all! Wanna help a KZbin 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 :)

[@whatamitalkingabout3]

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.

[@patrickjmt]

good luck! i hope you ace it :)

[@seansampler6808]

Thanks! Helped me a few hours before my final!

[@justinchey2281]

Same! I’ll probably find myself watching this video next semester too tho 🥲

[@Emmelifall]

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!

[@halvey8518]

You explained this 100x better than my instructor, thank you.

[@HS-jk8fj]

This question gave me 4marks in my online internal test today. Thank you very much.

[@cat_clawz9473]

This is a real big help! I need Calc 3 for Chemistry but that doesn't mean I have to like it. Thanks!

[@Debrizd777]

I was so frustrated I wasn’t understanding how to do this, this literally saved me from scoring a 0.

[@jetswhiteout961]

I have a final exam today and this helped a ton thanks!

[@123JustBelieveInMe]

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.

[@Gobljnn]

patrickJMT is the only reason why I'm passing University...he's going in my grad speech #phuckengineering

[@AyZeeCREW]

so, where are u now? did u pass

[@freakyyi]

@@AyZeeCREW XD

[@rantlord8373]

@@AyZeeCREW Silence indicates failure.

[@lubu2960]

@@rantlord8373 he ded

[@shradhabhadoria9575]

In india this is taught to a 16 year old student

[@fisslewine1222]

Explained really well , short and sweet.

[@gibsonlespaul5709]

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 KZbin 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!

[@ramanabalachandhran]

Thank you Patrick. This really helped. This is exactly what I was searching for. Best wishes!

[@smitaborole4404]

Thank you so much sir. This method really helped a lot

[@patrickjmt]

Most welcome!

[@Lexyvil]

Is there a difference between (...) and ? Aside from that, amazing explanation/refresher! Thanks.

[@orly6800]

God, u save my college life! Thank you soooooooooooo much!

[@therevenant4087]

You have no idea how much i love you.

[@nisalisadara6449]

Thanku so much. This was such a great help for my assignment

[@vibhavgangamwar6676]

Thanks…This is much simpler method than my JEE notes.

[@supeveryone99]

Good work mate. Thanks a lot!

[@royjacob8395]

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?

[@jesslarsen9624]

Thank you so much! This helped me on my problemset!:D

[@zlvidsNsoy]

you are great , you saved my life so harrrrd

[@firdauspuzi1145]

Do we need to expand them at the end?

[@Darkendscythepwns]

Thank you! This was very helpful!

[@hasanmothana]

thank u very much you realy helped me

[@serinacat4781]

Great video

[@danielcervantes8572]

great video, thank you

[@patrickjmt]

You are welcome!

[@hndrenG]

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?

[@bloojacket4284]

THANK YOU! text book was doing such a shitty job explaining...

[@dailyplanet8817]

Thanks I've been improving a lot lately

[@Ez252x]

You're the man!

[@steven9492]

i like this guy

[@EvalistusSimonT]

I thank you.

[@graemeosborne772]

How would you explain to a student why they need to find the normal to the plane?

[@Yuvi_isawesome]

Than you

[@poopie181]

Hi Patrick I have a very similar problem to this and am wondering how to solve it and wrap my head around it, I have three points A(α,1,1), B(1,2-1) and C(1,1,2) and am having trouble finding the vector equation, do you have any points? Thanks

[@pankhurithepunk8369]

First make out Cartesian from it for AB: X-a \ 1-a + y-1\ 1 + z-1\ -2 Therefore vector eq= ai + j + k + m( {1-a}i + j -2k) Similarly you can find for BC.

[@jenscmp]

thanks!

[@carlosenriqueulloa]

Most exelent!

[@krishnakadiyam2864]

but we can get different normal vector if we interchange the vector multiplication..and we get different plane.

[@Mr.Adhesive]

krishna kadiyam you are technically correct, but changing u x v to v x u would only make the result negative, meaning the plane is flipped 180. It's still basically the same plane. The only time this would matter is in computer science when calculating the visuals of a mesh, for example.

[@Monkyupurbutt]

This is an awesome video. Thanks! Very helpful.

[@Dezey.a]

What if instead of f(x)=0 it equals d as in another point

[@masateruhonest6908]

Just realized that a cross products is a computation of a determinant of matrix.

[@dipeshpatel1934]

Masateru Honest lol that’s the whole point of a cross product (algebraically atleast) 😂

[@shalvenic3948]

what if one of your abc values is a zero?

[@kantorobo7718]

thx m8 :)

[@Meownekox3]

why in general "u X (v X w)" and "(u X v) X w" are not equal (the associativity of cross product does not hold)? Lecturer`s counter example: let v and w be the same nonzero vector ( or any two parallel nonzero vectors) and u is perpendicular to both of them. Then u X (v X w) must be the zero vector since v X w is the zero vector. However, (u X v) X w is not the zero vector, because u X v is perpendicular to w. anyone can explain to me why v x w is a zero vector? =(

[@gavinburgess4374]

こんにちは! Any two co-linear vectors will cross out to be a zero vector. This is because the cross product is a way to find a normal vector between two nonlinear vectors by creating a parallelogram using these two vectors as sides. When both vectors are co-linear it is impossible to create such a parallelogram! I hope this helps, ねこにほんご.

[@Trekafied]

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

[@bballislife7158]

Patrick JMT is da real mvp

[@timolee8234]

bballislife7158 I'm guessing you go to a SoCal school too, perhaps UCSD or UCLA

[@bballislife7158]

Timo Lee You guessed right, but im in high school lol (calculus AB)

[@thewiseone9798]

+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.

[@bballislife7158]

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

[@djtsuna19]

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!

[@shrimatkapoor2200]

I love your vids because you go straight to the point unlike some other videos

[@GDarkGoombaG]

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

[@y.z.6517]

Thank you.

[@gomezalejandrog]

Like I understand the steps to do it, I just don't know what the numbers I'm calculating throughout the problem actually mean.

[@WHPH10]

Would the normal equation be the same if you picked different lines?

[@EnderKnightII]

because both of those lines still exist in the same flat plane

[@funnypakiserver2115]

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?

[@dmac201]

There is a matrix for what the signs are in a 3x3. I+ - +I I- + -I I+ - +I

[@skyfire1129]

Wow! You just released this yesterday, and my homework tonight is Exactly This! Excellent! You are a very generous person Patrick, thank you :)

[@MrRyancarr13]

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

[@feero9680]

3:16 does it always i-j+k ? I mean the j has to be negative?

[@apoorvajha6188]

Yes that's the rule

[@subarnasubedi7938]

We can do this more simply z=Ax+By+c is eqn of plane put (x,y,z) points in eqn produce three eqn and solve for A,B,C

[@manvinderbawa9597]

Kon kon lockdown mai es video ko dekh rha hai?😅

[@curtistrinh5654]

to be honest this doesnt make sense to me, it just feels like im copying the same formula over and over, how are these equations supposed to equate to some visual representation of a perpendicular equation. I guess the parametrized equation uses the vector like an initial value similar to an y = mx+b and these parametrization is accounting for a equation not in 2D space but 3D space? i just dont rlly get it and theres so many equations that i think my cheatsheet is full.

[@dunjiyungmean6617]

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.

[@smurfolissicus]

Thank you SIR, calc professors with positive attitudes make a funner and easier learning environment!!!!

[@valizeth4073]

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?

[@ValerieAyala1]

wonderful explanation!! Thank you, you have saved me from stress:)

[@fraserglasgow5735]

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

[@norabseven]

Your explanation is absolutely top tier... I just... wish you were right handed..

[@rimiadhikari7973]

Thank you Patrick! I'm a student of class 11. Love from India 🤍

[@sharonsolana]

Does anyone want to know a _much easier_ and less time consuming method of finding the cross-product?

[@mahekparmar5193]

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?

[@chrishayes9978]

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.

[@patrickjmt]

make a cool game for me! :)

[@telracsazyl1243]

thanks for the info bruh. im stuck with vector because i cant study if its not face to face. have a great day

[@PraiseTheSquid]

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

[@tyswid]

Being a freshman in College taking calc 2 this is a very helpful example.

[@omarmavs]

Love your tutorials. Hate how you're left handed

[@yasarkaya8176]

Thank you Patrick ! This video really helped me to solve my calculus problem. :)

[@YDYoshi]

i thought to find a perpendicular line we must do the dot product. not the cross product right?

[@markliberman3399]

Thank you very much for this :)

[@patrickjmt]

no problem!

[@DoggoWillink]

The thing that annoyed me about multivariable calculus is that they use the words perpendicular, orthogonal, and normal all within like ten pages of a text book. Perhaps I'm wrong, but they all mean the same thing as far as I know. Why not just say normal (since they use normal in physics the most), or perpendicular (which is known by most people).

[@louismayco507]

is it necessary to use P as the "point on plane"? or u could use either Q and R ?

[@theoutsmarter7662]

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.

[@isaliu]

Hi Patrick! First, thank you for providing all this helpful information. Can I ask, does the two parallel vectors have to share a common point, which is the point used in the position vector? For example, with points A, B & C, can I use r = OA + n(BC) + m(BA)? instead of the usual r= OA + n(AB) +m(AC)?

[@williamfrederickgates2088]

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

[@SkyEatsSpaceShip]

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?

[@sirinorthpaw3993]

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

[@gothveggies]

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?

[@adaml929]

This saved my life, you rock! Part time AP teachers should not be allowed...

[@RaagDawg11]

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! 🤩🙌🏻

[@nanopocoyo]

how about this: find the eq. of plane that passing through points (2,2,1) and (-1,1,1) and perpendicular to the plane S:2x-3y+z=3.

[@tangpiseth8416]

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!!

[@crayzchic91]

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?

[@GraceCleo]

Bless. Pre-Calc is killing me. (Trig, however, was fun.)

[@beckwilde]

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?

[@kkcheah6402]

Thanks for the video. It really helps me understand more about vectors and planes. Thank you so much!

[@canadiannuclearman]

Thanks. This could have helped me in my work with finding the press break angle in sheet metel. This shows the first part. Finding the equation of a plane then finding the angle between planes is great for sheet metel work. its faster and more accurate then using trig or applied geometry in finding the dehedral angle.

[@12as34df5]

I just want to say, THANK YOU because neither my teacher or the textbook covered this.

[@kiwilitious]

you sir have made my day

[@harshitkhanna1918]

Just use scalar triple product =0😂😂😂

[@brixter1232]

can i use the subtracted point PQ to find equation of plane instead of using point P?

[@11baroda]

Lol its my finals now and after a year im back to cram... u da real MVP