How To Find The Distance Between a Point and a Plane

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.

Triple Scalar Product:

Vector Equations of Lines:

The Equation of a Plane:

Planar Equation - 3 Points:

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Lines & Planes - Intersection:

Angle Between Two Planes:

Distance Between Point and Plane:

Chain Rule - Partial Derivatives:

Implicit Partial Differentiation:

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Directional Derivatives:

Limits of Multivariable Functions:

Double Integrals:

Local Extrema & Critical Points:

Absolute Extrema - Max & Min:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[amyturner]

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

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[jacobhellenbrand]

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[georgesadler]

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 YouTube TV with the Organic Chemistry Tutor.

[stridebird]

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.

[leopoldcrouse]

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[m__a_]

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[ThShrike]

love how straight to the point the video thumbnail is

[Smc-to]

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

[zengyuanable]

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

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[karanveercheema]

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?

[kenzyatef]

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 ?

[muhammadnevin]

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

[hoanglong]

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.

[shyamss]

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?