Equations of Planes: Vector & Component Forms | Multivariable Calculus

We will come up with first the vector form of the equation of a plane, and then expand to get the component form of the equation of a plane. The formula is based on knowing:
1) A point on the plane
2) A normal vector to the plane

Planes are foundational objects in multivariable calculus (for instance, the analog of a tangent line for functions of one variable will be a tangent plane for functions in two variable).

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This video was created by Dr. Trefor Bazett

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[pi_academy_manipur]

This is the only video which explains intuitively about plane Equation in whole YouTube

[smizmi]

going straight to the example was so helpful. After years I finally feel like I could work with planes. I feel so powerful.

[txnwqnn]

Honestly, thankyou so much. I have watched probably 2-3 hours worth of videos on this topic, trying to understand it and failing. Your video has made me feel like I can fully grasp planes.

[stvs]

I have watched a lot of math videos in my life... Your videos are beyond excellent. Thanks for the help.

[master_zenrade]

Thank god I found these videos on time. Otherwise, VIT would have killed all my mathematics appetite.

[AmirJacob_]

I always watch your videos whenever I'm having trouble understanding a new concept!
Grateful to you for the effort you put in :)

[itskarim]

One cant memorize but only viusalize. Thanks alot

[LevySkulk]

I hate how simple much of math is to understand once it finally clicks. The textbook I'm using is woefully lacking in examples or nuanced explanation. It's almost like it assumes you already know what it's talking about, very frustrating. I'm only on R^2 vectors but your explanation applied to the normal definition of a line as well.

Your explanation starting at 1:40 finally made everything make sense. I could not understand how this equation was defining a line, did not make sense to me. I now understand that its sort of defining it by exclusion.

n * (x - p) = 0

P can be the origin, or another arbitrary point on the line. n is just another vector, which mean any vector x which is orthogonal to n is part of the set which is defined by the line, or in this case the plane.

Thanks for this video, I like how yo explain things. A lot of math instruction assumes students already know how to think about concepts in a specific way, and provides explanation in a way that fits into that framework. I wish textbooks would attempt to give a plain English overview of an idea before diving into proofs and formulas, a simple paragraph attempting to explain the idea without any variables or numbers would have done wonders.

[alexmassy]

Yes. Perfect. Thank you to explain it so well and intuitively

[scope]

So easy to follow! I have been somewhat lost for the past week since starting the semester and this video helped me out a lot!

[tevinabeysekera]

Thank you so much for the simple explanations and useful pictures. My professor spends 50 minutes showing complicated theorems and definitions that are hard to understand.

[zahoormuhammad]

Thanx for such a nice short and to the point information

[Malikuzaif]

First time I see nice explanation in you tube and on the point to take us example ☺

[continnum_radhe-radhe]

Sir please make videos on multivariable limits, jacobian, taylor series, maclaurin series

[oluwasemilogobalogun]

What textbook would you recommend to study vector line

[RubenHernandez-fqys]

You could use the normal vector method to determine the equation of a line in 2 dimensions, correct?

[malakasadalikhan]

dot product is always zero when two vectors are perp. to each other... n vice versa for Cross Product?

[zac]

can you give me some sources of exercises to practice math problems?

[amrelshabasy]

This is a great video. you just made it very simple.

[TaniaHeller]

but what is the meaning of the constants?