Distance Between Point and Plane

Finding the distance between a point and a plane means to find the shortest distance between the point and the plane. This is made difficult due to the fact that we don't know the point on the plane that is closest to the point in space. It turns out we can compute this distance using a projection vector, which we discuss.
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[@mscottbarnes]

Just joining the crowd. You make it sensible and obvious. I shopped 6 other UA-cam videos. It helps you don't constantly restate what you're writing.

[@fireflylectures]

Thanks Scott! 🙏🏼

[@msz262]

Man you're simply the best. Here i am in a one man standing ovation for such brilliant, concise and clear lecture. Your effort is not in vain, please don't stop making videos.

[@fireflylectures]

matheus zarro Nice! Glad you enjoy the videos. Have a great day! :)

[@pawelsliwa6191]

I rewatched several of your videos now preparing for a test, this one stands out as the best one to me. Make with that what you will :)

[@martinibomb]

Dude your so concise and you always explain why shit works it's beautiful and so helpful, I love ur lectures

[@Farreach]

thank you so much man ..your a life saver for my linear algebra class

[@jdlopez131]

this is the best video I found... but, I have a suggestion. So far we've seen vectors projected that start from the origin. PQ does not start from the origin and that creates a bit of confusion. It would nice if you could explain that P-Q is actually the vector from the origin, and then just proceed with the projection calculation as usual. That tiny step made a mile difference in my understanding.

[@ajmalrashid]

Very clear and wonderful explanation. Very helpful.

[@Yusuf-un6md]

you explained it so well. Thank you very much.

[@srjit_]

Thank you, sir! Very clear explanation.

[@eliaswallin3145]

Your videos are awesome. Definetaly the best videos on calc 3 I've seen on youtube. I f*cking love you.

[@lukehatcher98]

amazing explanation, best ive found on yt

[@covfefe2936]

Thank you very very VERY much. Simple explanation for a complex concept! ♡♡♡♡

[@nemathassnain8522]

Sir! Thank you so much. Simply the best

[@SimpleLivingHigherThinking]

Thanks for such simple and clear explanation !!!!😀

[@gracenicola3270]

I appreciate this so so much I have watched so many videos on this and after watching yours I finally understand how simple this actually is! Thank you so very much!!

[@fikret8422]

you are great i found this chanell by chance but i m sure i will not regret because of coincidence

[@markcavendish7148]

Very nice. Please continue the good work.

[@cassidyo5541]

This is fantastic! My professor does no examples! Super clear!! Easy to understand! Thank you!!!

[@smith1228]

Another brilliant video! I wish I would have found you sooner, you have rescued Vector Analysis for me. Where have you been? Why do you only have 1000 or so subscribers and PewDiePie has 4 million? What does this mean for western civilization? Why, why, why!

[@fireflylectures]

smith1228 - Ha! I wish someone would explain that to me! Thanks for the kind words, and good luck this semester. :)

[@kelvin8923]

A lifesaver. Thank god you exist!

[@ahmedelsabagh6990]

Excellent explanation

[@himeshdrox1]

awesome lecture really appreciate your effort!

[@fireflylectures]

himeshdrox1 - No problem! :)

[@dedeks3000]

Very elegant explication.

[@rhetorical_]

could the distance formula be rewritten as the dot product of PQ and the normalized version of vector n ?

[@ericwu6428]

Wow. I am someone in Algebra 1 and I could at least follow along. Very well explained.

[@fireflylectures]

Eric Wu very impressive Eric! Good job!

[@ahmedelsabagh6990]

Great explanation

[@mamadetaslimtorabally7363]

Could I give you a question on Vectors to solve please. No obligation. Thanks.

[@nunu.g]

thankyou sir ,that was very precise. '

[@shudidesai]

This was awesome. How would you do distance from a plane to a plane?

[@uzmaimam8911]

Distance between parallel planes are same as perpendicular distance between a point and a plane.

[@h_ar_ou_n5149]

If you were given equations of 2 paralle planes, would the distance be the magnitude of the normal

[@palakkapoor5586]

How to find the coordinates of that point on plane which is at a D distance from the given point? Please help me.

[@rikenm]

I want to know how do you know that the magnitude of projection of PQ to normal vector is exactly same as the distance from the plain to the point? Thanks for your videos. I would say they are 100 times better than my professors' lectures.

[@jdlopez131]

lol... that's what the video does... what part are you confused about ?

[@sandorfogassy3007]

Well done.

[@piravythan934]

Why didn’t you take scalar projection directly?

[@abu_staif]

My only complaint is that I did not find this video sooner!!!!

[@DAaaMan64]

Are normals being a vector of length one just a computer science thing? If not, then couldn't we simplify this further to just Distance = abs(|PQ*n|)?

[@uzmaimam8911]

Yes you can.

[@BGFutureBG]

I don't quite understand the division by the normal vector's magnitude in the final formula. Isn't the magnitude of *n* always 1 as the normal vector is normalized?
(Possibly stupid question, beginner here, sorry)

[@cemrekeles2032]

magnitude of n is not 1 for most cases. n is just a perpendicular line to the plane.
It is not a stupid question, ı also thought the same thing and try to figure out. Good luck.

[@jachpriboi2580]

Thank you! :)

[@fireflylectures]

Jach Priboi - Welcome! :)

[@ye3258]

Clear

[@pawelsliwa6191]

favorite lecturer too bad only covers few of my topics and tehy are mostly niche once

[@madhumithaayyappan5277]

THANKS

[@Tombalino]

thankyou

[@mbordiermontes]

are you anklespankin's dad?

[@noble64890]

what is N. if you mention it, explain the unknown!

[@user-bd3vc6ih1z]

Thanks

[@snikkers83]

elegant :)

[@Mannnee]

What is the difference between magnitude and absolute value. Isn't it the same thing?

[@sharonsolana]

Magnitude is length.

[@hibanerd4822]

I ❤ ed it

[@jamesrockford2626]

great

[@fireflylectures]

James Rockford - Not as great as that hair, man. Rock on! :)

[@jamesrockford2626]

Firefly Lectures yeah.. Paul Kossoff had great hair

[@jamesrockford2626]

Firefly Lectures
Can you do a tutorial on how to project a point, perpendicular to a plane?
so you can find the intersection point?

[@fireflylectures]

James Rockford Hmm.. that's interesting. I think this should work:
1. Find the normal vector to the plane.
2. Write the equation of a 3D line in space with the direction vector found above, that goes through the point P.
3. x, y, and z for the line are now all in terms of t. Take each function of t and sub into the equation of the plane for x, y, and z. Equation of the plane should now only be in terms of t.
4. Solve for t.
5. Plug that t into the parametric form of the line to find the (x,y,z) point.
*You can confirm this is the correct point by doing the distance formula from this point to point P and seeing if you get the same distance as we got in the example video that follows this one.
Let me know how it goes :)

[@jamesrockford2626]

Firefly Lectures
thanks I'll try it, appreciate it

[@footballisahumbler]

BOOM!!!

[@A-R53]

May Allah bless you 🌹💐🌺

[@hafsaimtiaz5832]

Is this for edexcel pure maths 3

[@junkemail3769]

Broooo

[@hunterhalvorson6223]

goat

[@sharonsolana]

A math smart aleck!

[@vedarn123]

He looks like the tall guy from dude perfect.

[@abdullahfawadkhan5040]

Half the lecture is wasted on explaining that we have to find perpendicular distance, dude it’s given in the question