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How To Find The Distance Between a Point and a Plane

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This Calculus 3 video tutorial explains how to find the distance between a point and a plane using the dot product formula and scalar projections of vectors.
Area - Vector Cross Product: • Area of a Parallelogra...
Triple Scalar Product:
• Volume of a Parallelep...
Vector Equations of Lines:
• How To Find The Vector...
The Equation of a Plane:
• How To Find The Equati...
Planar Equation - 3 Points:
• How To Find The Equati...
_______________________________
Lines & Planes - Intersection:
• How To Find The Point ...
Angle Between Two Planes:
• How To Find The Angle ...
Distance Between Point and Plane:
• How To Find The Distan...
Chain Rule - Partial Derivatives:
• Chain Rule With Partia...
Implicit Partial Differentiation:
• Implicit Differentiati...
________________________________
Directional Derivatives:
• How To Find The Direct...
Limits of Multivariable Functions:
• Limits of Multivariabl...
Double Integrals:
• Double Integrals
Local Extrema & Critical Points:
• Local Extrema, Critica...
Absolute Extrema - Max & Min:
• Absolute Maximum and M...
________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

Опубликовано:

29 авг 2024

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Комментарии : 135

@TheOrganicChemistryTutor 7 месяцев назад

Final Exams and Video Playlists: www.video-tutor.net/

@kkhalid6409 4 года назад

i feel like this guy will go straight to the heaven just because the number of engineers he molded

@user-wr8yg8ix6r 4 года назад

Engineers, math students, science students, and even highschool students...he'd literally be in the highest level of heaven

@juanmanuelmillansanchez8165 4 года назад

yup, not only his contry's but worldwide

@wbaatz 3 года назад

@@user-wr8yg8ix6r insha Allah he will be. May God make his life easy, and give him a courage to stand against hard times. Ameen.

@Snowman4PF Год назад

HMMMMMMMM😂

@Snowman4PF Год назад

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@amyturner2635 3 года назад

It's really helpful when you go back and explain where the formula come from, rather than just use them. Thank you

@imanhosseini6908 Год назад

Man the impact you've made on the world is grandly incalculable

@ezellstewart3894 4 года назад

Took my general chem 1 ACS today and got an 82 without your videos I don’t think that would’ve been possible without your help. Thank you sooo much!!!

@vashon100 8 месяцев назад

You got an 82 without his videos? Or maybe 2 sentences?

@mohammedomer3565 2 месяца назад

bro said WITHOUT your vids and then went on to score 82 and THEN BRO SAYS THAT HE HELPED HIM Is bro HIGH??

@jacobhellenbrand3128 4 года назад

really love your videos, they've helped me a lot in understanding my compacted ap calc class, keep up the good videos!

@broth9712 4 года назад

Jacob Hellenbrand yesterday was my test this dude just saved my head

@m__a_ 3 года назад

The way I can understand concepts by watching your video always amazes me. Because I understand the math but no the concept with my professors and I just need to watch your videos and I'm all set. THANK YOU!

@georgesadler7830 Год назад

Professor Organic Chemistry Tutor, thank you for deriving the mathematical formula that is used to Find the Distance Between a Point and a Plane. Deriving formulas in Mathematics increases my knowledge/understanding of the material. This is an error free video/lecture on RU-vid TV with the Organic Chemistry Tutor.

@stridebird 10 месяцев назад

It's very neat how we start by defining a P0 and it then disappears leaving just the components of P1 in the final formula. What a plot twist! Nice video - thanks.

@Smc-to 4 месяца назад

Thank you very much for showing us the easiest way we can solve such these problems

@leopoldcrouse5085 2 года назад

This just helped me solve a problem I had spent 4 hours on. Your vids are Khan academy level or better! Thanks!

@Th3Shrike 3 года назад

love how straight to the point the video thumbnail is

@Migixkem 4 года назад

ur so helpfull and determined God bless you

@zengyuanable 2 года назад

thanks for the video! it has helped me through so many difference topics (differentiation, integration, laplace trans, matrix, vectors etc)

@anastasiaanautodidact9856 3 года назад

His voice... Is the most soothing

@itsMNiz Год назад

From the bottom of my heart.. I owe you my life

@hamzamunir6526 4 года назад

🔥🔥🔥 You are on another Level Learning Soo much from your channel Thank You Unknown Sir

@karanveercheema2975 2 года назад

3:14 why did you have to do the projection stuff instead of forming the triangle between points p0, p1, and the point where D touches the plane? And then you can get the trig identity costheta = D/|B| and then rearrange for D= costheta*|B|? What was the purpose of the scalar projection of B onto N?

@Dina-he1uc 4 года назад

thank u so so so so much what would i do without you

@hoanglong5824 3 года назад

Concretely, I think the reason why ax0+by0+cz0 replace by ax+by+cz is because P0 is in the plane ax+by+cz=-d, thus they are equal to each other. btw, insightful explanation.

@Kosmonutty 11 месяцев назад

I was taught with a positive d on the right side because it doesn’t matter. You just replace the form ax+by+cz with whatever is on the right and don’t have to worry about 2 sign changes.

@Kosmonutty 11 месяцев назад

Alternatively you can think any point on the plane satisfies ax + by + cz = 10 so you can replace the second grouping corresponding to the point on the plane with 10 so you don’t get confused by the sign of d.

@heathc148 11 месяцев назад

God bless you brother Jesus loves you

@kevinocampo3605 4 года назад

When u doing a face reveal

@assaultszn3557 3 года назад

sus

@kenadams9024 3 года назад

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@green_razor8569 2 года назад

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@wanderingpalace 2 года назад

@@green_razor8569 imposter

@xLynxxx 2 года назад

AMONGUS

@cathrinemwangemi12 2 года назад

May God bless this man.

@muhammadnevin564 3 года назад

Hey Dude, your explanation is amazing. I want to ask, how to find the closest point from a point to a plane or line. If you've explained it in another video, please let me know. thank you

@bossricewallis5132 Год назад

I don't think he's gonna let you know

@mohammedhamza8492 3 года назад

Awesome explanation

@jingyiwang5113 6 месяцев назад

Thank you so much for this amazing video! It is really helpful!

@shyamss2338 3 года назад

Why are we considering the plane 6x- 3y+2z= 10 to be equal to n vector instead of the horizontal plane perpendicular to point p as depicted in the video?

@berraurhn 2 года назад

same questionnnn :( ?

@vealtt 4 года назад

Why not just find the line equation (we have direction and position vectors already)? We then substitute x, y and z of the line into the plane equation and solve for the paramater. We then obtain the parameter that we can use to calcualate the point that lies on both plane and the line (which means exactly under the point we are looking for). Then simply calculate the distance between two points and we have the solution.

@kenzyatef7366 2 года назад

I have a lot of questions.. why is n a,b,c isn’t n a normal vector and a,b,c is the equation of the plane ?

@lok2ky Год назад

dude, you're genius 😎

@gabrielmakenmuno4165 4 года назад

Very helpful Sir thanks alot..........btw, what if there are two plane equations, how do you go about solving them?

@CarloLavezzari 4 года назад

Are you sure D should be -10 and not +10?

@princembua3622 Год назад

IAppreciate all your videos sir

@xaoqi1157 3 года назад

you always save my life

@iangomez7190 2 года назад

I love you ochem tutor. I will die for you

@benmontgomery1111 2 года назад

makes sense! Thanks!

@Sara-md8nu 4 года назад

Does anyone know if he does statistics videos? He helped me get an A in algebra1 and an A in algebra2. Now onto stats next semester which I haven't a clue what I will be learning 🤯

@anasasim3856 3 года назад

he does! Search it up please

@lx7340 4 года назад

Can you please do a video on Commercial Arithmetics (Tax)?

@benedictding Год назад

Thank you for the video, very helpful!

@alexzhang3761 Год назад

well explained, thank you!

@user-oj6un5ci8g 3 месяца назад

I love you. So much. You have made math so powerful and fun in my puny little brain. You better be making millions of dollars from this.

@trapfish1217 Год назад

My hero!

@morjes152 2 года назад

Thank you so much man

@eldaralizade1707 2 года назад

You are the best! I mean it.

@GuitarFable 11 месяцев назад

thanks !

@user-qr4rv7ng8n 2 месяца назад

Thank

@seradfb345 2 года назад

00:02:25 where he says "D is the absolute value of the scalar projection..." he writes "D = comp n B" on the blackboard. I'm not sure what that means exactly or did I misread what he wrote. Anyone have any idea?

@VenkataB123 2 года назад

So, if you dot B and n, you'll get the projection of B onto n (which is basically what dot product is). But, if you see carefully, the projection B makes on n is equal to the distance D. That's why he wrote D = comp of B on n

@karanveercheema2975 2 года назад

comp = component?

@VenkataB123 2 года назад

@@karanveercheema2975 Yup

@Raven_Ray1 2 года назад

Thank you sir

@sileshiabebe8605 3 года назад

Even God can't explain like you!

@thitipongthitipong3354 3 года назад

Thank you

@hangkertzy9722 3 года назад

thankyou so much

@AkimboFennec 2 года назад

Why is vector n = (a,b,c) parameters of the equation of the plane? How do you know it?

@earthpongsapak7706 3 года назад

Thx

@tinalgh4636 5 месяцев назад

Please teach vector analysis

@passakornb1680 3 года назад

thx so much

@tinashemasoka8843 Год назад

might actually pass my linear algebra midterm now

@EC-pf1tr Год назад

cool derivation thx

@Obliviousovertimer17 3 месяца назад

if it is as you just said, the magnitude of n should be equal to the distance b/n the point and the plane, i don't get the logic

@kylejohnson1248 2 года назад

What happens if the point is not perpendicular to the plane ? Would you still be able to use the scalar projection of b onto n to find D (the distance)?? Anybody know ???

@GaryTugan 3 года назад

excelent vid!

@kifter4254 4 года назад

Please do more videos on AC electricity

@namanoinphithak3102 3 года назад

verygood thanks bro

@naynay4058 4 года назад

Must the line the point makes with the plane be normal to the plane?

@ahmetkaansever6439 2 года назад

yes that's the shortest distance

@user-wr8yg8ix6r 4 года назад

I love u man):

@RaffaelloLorenzusSayde 2 года назад

What about the shortest distance from a line to a point?

@joelkagamba5696 9 месяцев назад

the goat

@satyampandey2222 4 года назад

Good one bro

@osorepurity Год назад

How do I find k if the distance k,0 and 2k,0 is 10 units

@sutatthepsingkhudron6832 3 года назад

Thx guy

@alexanderaladin1328 Год назад

Please explain how we got d, i got everything else

@PaaPhum 3 года назад

ขอบคุณค้าบบพี่เสือ

@mizgintusgul8089 3 года назад

sorry, why was the denominator the square root of a^2 +b^2 + c^2 please? why is this put in the formula for D, or just from a standard formula?

@gokulkpeethu6642 3 года назад

The distance of a point n with coordinates (a, b, c) from origin is denoted by |n| and is equal to sqrt(a^2 + b^2 + c^2). This is from the equation of distance between two points and substitute the second point as origin i.e (0, 0, 0)

@mizgintusgul8089 3 года назад

Oh, okay thank you so much, so he substituted the n in, so we have to generally know this square root part or do you know how it was derived, i don't want to confuse but would it be from the a^2+b^2=c^2 formula? Thanks

@leldeslaidina1963 3 года назад

I don't understand why vectors a and b were then compared to vectors n and B, if n is taller then a?

@dionysiandreams3634 3 года назад

Damn these videos from "2006" are helping

@ohmmy6826 3 года назад

Thank you

@chanchondipracha4360 3 года назад

thx

@TheDaniel85 2 года назад

I wish I had just followed your videos and not spent weeks trying to decipher our damn textbook, written by a mathematician, for mathematicians... not for students.