Distance between parallel planes (vectors) (KristaKingMath)

► My Vectors course: www.kristaking...
Learn how to find the distance between the parallel planes using vectors. Verify that the planes are parallel by finding the normal vectors to the planes and proving that the normal vectors are parallel. Then find a coordinate point on one plane, and calculate the distance between that point and the other plane by pulling the components of the normal vectors, and the values from the coordinate point into the distance formula.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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[@nicolenelson9180]

I've been using your video's since Calculus I, and now I'm in Calc III. I always thought I was terrible at math an could never do it. But now I'm so far and I still can't believe it. Thank you for making all these videos!

[@kristakingmath]

+nicole nelson Thank you so much for sharing! It made my day. I'm so glad I've been able to help along the way.

[@Schytheron]

You are one of the best online teachers I have seen. Your explanations are very simple and easy to follow. I hate teachers who over-complicate their explanations just for the sake of sounding fancy...

[@kristakingmath]

Aw thanks! I'm glad you like the videos!

[@HP97user]

Thank you for walking through every single step and not skipping any nuances. It really helps be know where every number came from.

[@kristakingmath]

I always hated when steps were skipped, so I do my best not to do the same. I'm glad I could help!

[@ryan2009cov]

Takes a bit of time to wrap your head around, but this is the best explanation of distance between parallel plains available on RUclips.

[@absolhonk7804]

thank you for your videos. You and Organic Chem Tutor are keeping me afloat in school.

[@ramanahlawat398]

The shorter method would be by multiplying eq 1 by 2 so that the coff become same then apply the formula.
let const term in eq 1 be x
and in eq 2 be y
so d=(x-y)/√(a^2+b^2+c^2)

[@briangonzalez6432]

I know I’m insanely late but this was a struggle for me and you made it more simple for me. Thank you. You’re the best

[@kristakingmath]

Aww, thank you so much Brian, I'm so glad this helped!! :D

[@Enes-hr3hp]

THANK YOU SOO MUCH. your voice makes me wanna learn :)

[@kristakingmath]

You're welcome, Abdullah!

[@muhammadabdullahnaveed3216]

I have my final in just a couple of hours and you legit just saved my semester

[@kristakingmath]

I hope you did great on your final, Muhammad! :D

[@thehelpfulshadow919]

This video is a lot more helpful than my textbook. Especially the easy to understand distance formula. I sat here for 20 minutes trying to figure out how to understand d=abs(PS•(n/|n|) with PS being a vector connecting a point to a plane before I found this video.

[@kristakingmath]

I'm so glad it helped! :)

[@bhavesh.adhikari]

thanks! just curious why did you set y=z=0 , cant i did the same for x,y and solve for z ?

[@MohsinOmar]

Spent 3 days trying to figure this out as the textbook did not explain anything. I would just like to thank you so much for this video!!

[@Bedocalaway]

THANK YOU SO MUCH! Going to write my exam in a few mins now xD

[@fr0z3n2]

This is the best tutorial video ever! This should be the standard.

[@kristakingmath]

Aw thanks! 😊

[@manakparmar1793]

Very nice explanation👌

[@ray93950]

Very clear and intuitive video! Exceptional! Please keep making more and more, I love your style

[@kristakingmath]

Thank you so much!

[@YoshevElazarMikael]

i'm in love with your teaching

[@zabilonlukas]

thank you, krista. for clear explantion

[@rxlvnd3397]

Thank you so much Krista!!

[@kristakingmath]

You're very welcome! :)

[@xikasprrzz3777]

Thanks. That is more than clear.

[@kristakingmath]

I'm so glad it helped! :)

[@briemann4124]

Probably it has been pointed out, but just a heads up that you abuse notation a little (you've used 'd' on both the left and right-hand sides of the equation, but they represent different things).

[@karencovey7123]

Thank you Krista. Such a good explanation and so clear. You are a really good teacher! Putting up a link to your for my video students to watch. :)

[@kristakingmath]

Thank you so much, Karen, I'm honored! I'd be happy to help your students in any way that I can. Thank you for what you do! :)

[@alialoraini5733]

Thank you so much Krista for this amazing explanation. Greetings from Saudi Arabia!

[@kristakingmath]

I'm glad it could help Ali!

[@scotthackney4747]

Great video, thank you!

[@kristakingmath]

My pleasure! So glad you liked it! :)

[@shreyamduggal1919]

after watching 100 videos for this problem finally got a nice explanation thanks dude

[@kristakingmath]

Yay! Glad it could help.

[@dineshpethad5856]

Very good explanation

[@dionpiex]

Thank you very much. To be honest, you teach better than my teacher. Wish you could be my algebra teacher. :D

[@kristakingmath]

I'm just glad my videos are helping! :)

[@willeett]

Fast paste and good. Thanks.

[@fastfurious82]

This video was helpful, Thanks.

[@gieseanw]

Re: finding a point in the plane. What if the plane doesn't cross the x-axis? That is, x=3 for all points in the plane. What would our plane equation even look like then if not like a line equation?

[@Kali-bs7oj]

If you can just pick a point, isn’t the distance you get pretty arbitrary? Like there are an infinite number of distances from each point to a location on the other place. Just wondering, I think I’m missing somethjng

[@a-vinil]

An even shorter method is by using this formula: *_distance=|d2-d1|/sqrt(a^2+b^2+c^2)_* . d1 and d2 are the constants in their respective plane equations.

[@ryuurena9787]

Nice video and very helpful. Can I know the real explanation why Y and Z is equal to zero when you want to find the point on the plane? I just want conformation.

[@Fadic4]

do you remember when you had a equation for a line back in algebra and you wanted to solve for x so you would make y=0 or if you wanted to solve for y you would make x=0 i think its the same concept but in 3d

[@trynow8915]

Thanks 😊

[@puffponken4711]

Great explanation! :D

[@lux_cyber_soldier]

I love you Krista

[@oliviascully1087]

thank you so much , very helpful video !!

[@techvlogs7187]

thanks a lot,that was crystal clear

[@kristakingmath]

So glad it helped! :D

[@KampungJering]

Greetings from Singapore. Very helpful, thank you!

[@kristakingmath]

+Peter Siau You're welcome, I'm so glad it helped!!

[@curtisjaekl1824]

I have a question you may have said this in your video but would. just want to say this again to confirm we can use this idea to find a the distance between a parallel line and and a plane?

[@PhaeronServinus]

you're a miracle worker, thank you so much

[@prathvisingh8288]

Such clear explanation 😍

[@kristakingmath]

Glad you think so! :D

[@capone9905]

and also in finding the points can also find other intercepts apart from the x intercept?

[@jamesharding3182]

this actually worked completely differently to my textbook lol nice one

[@Chrome47]

#73 from section 12.5 in Stewart 7th edition!! Thank you!!

[@Unforgivable43]

Thank you, you really know your stuff.

[@oneinabillion654]

Hi, could u make a video on other methods to find the distance between two planes?

[@capone9905]

please in find the points can you use any of the planes?

[@pratikkothari873]

Are there any more videos of you about different formulae of plane?

[@Sonn_of_Zion]

wow great explanation.

[@punk199615]

Thanks! I have my final tomorrow and I am trying to cram 4 chapters of information in 26 hours!

[@kristakingmath]

Oh no! That's never easy. But it'll be over soon, and hopefully you rock the final! 💪

[@pratikkothari873]

best video...very helpful....thanx alot....✌👍😀

[@kristakingmath]

+Pratik Kothari You're welcome, I'm glad it helped!

[@intelligentinvesto9060]

The title is distance between 2 parallel planes. But in the video it is distance of a point from a plane

[@andrewscott9088]

we chose a point on one of the planes and found the distance from the other plane to that which is same as the distance between the two planes

[@supersonic174]

this did not work for me, one of the planes was = to 0 which is different to your example. Other thing is that confuses me is that, what point on the plane? because you could have many points, and you would want the shortest wouldnt you?

[@ahmedaldakhoul5093]

It is such a good way......thank you

[@kristakingmath]

+Ahmed Aldakhoul You're welcome!

[@pavanakumarmohanamuraly6433]

Bad choice of variable names "d" denotes both distance and coefficient ! Quite confusing ...

[@halbrd]

Brilliant. Thank you.

[@kristakingmath]

Glad it could help!

[@MurraySwe]

Very useful video, thanks. :)

[@kristakingmath]

+MurraySwe Glad you liked it!

[@rinkityagi4155]

thank u so much. it really help me out

[@kristakingmath]

You're welcome, I'm so glad it helped!

[@siddhantkate5305]

LOVE FROM INDIA 🤗

[@riyarelan2588]

wow :O amazingly explained. thanks

[@kristakingmath]

+RIYA RELAN Thanks! Glad it could help!

[@MatthewTurner-vk6hn]

Very good job. But you have too many d's . And you can not pull out a negative 2. Negative 2 is not available to pull out in the end.

[@danielagarciazepeda416]

Thank you! You make last minute studying for a midterm easy.

[@botofwar6567]

You’re the best 🙌🏻 💯👍🏼

[@kristakingmath]

Awe, thanks! :D

[@ايمنالحربي-ب2ش]

Thank you

[@A-R53]

Thank you so much!
Very simple but useful :-)

[@kristakingmath]

You're welcome, I'm so glad it helped! :D

[@yonnyboy3]

Life saving video

[@kristakingmath]

+yonnyboy3 :D

[@sammy5576]

thanks

[@indubagade9560]

You are just amazing....thanks a lot😄

[@kristakingmath]

You're welcome, I'm so glad it helped! :D

[@minhaj9802]

Why not just mutiply the first plane equation by 2.Use d=D1-D2/Square root (A2-B2-C2) A,B,C would be equal. You need not have to find 2,0,0 and multiple ax1,by1,cz1 and would have spared a minute and half of the video.

[@nkosinathimaphanga5450]

great stuff.. thanks a lot..

[@kristakingmath]

you're welcome!

[@Nurbolotadylbekov]

Sorry...Which program are you using on PC? integralCALC

[@fouadhaidar3640]

Thanks. You're awesome!

[@kristakingmath]

I'm glad it could help! :)

[@clavanya6403]

Thank u soooooooooo much.

[@allupinyomine]

this video is the reason i passed my quiz

[@jatindersinghbhatti4308]

You are awesome; thank you.

[@kristakingmath]

+karan singh Awww thanks, you're welcome!

[@fannywiman5992]

how do you know that the normal vectors are parallel ? just because their ratio is the same? i dont get it

[@bahaatamer1245]

if any 2 vectors are parallel, when you compare all their coordinates (x,y and z) they must give you a scalar that is the same for all. If they do not, they are not parallel (the scalar here was lambda in her video)

[@zedmontage1701]

Thanks a lot :)

[@kristakingmath]

You're welcome, Zed! :D

[@Ahil4421]

why don't we just take the magnitude of the normal?

[@i_akshaybabu]

Thanks it help me so much😃😃

[@kristakingmath]

You're welcome, Akshay, I'm so glad it helped! :)

[@sisosos7683]

thank you ...how can i find the distance between two skew planes ?

[@uristits]

Theres no such thing as skew planes....

[@sagnik4293]

I have a doubt

[@Wajahat-khan786]

Love you dear ❤

[@muhammadtahirrana4666]

you saved my quiz today....

[@kristakingmath]

Oh good! I'm so glad it helped! :)

[@emilio.squats8919]

Vid starts at 3:09 thank me later

[@kavitakumbhakar7220]

Thank you so much ❤️ tomorrow is my exam 😥

[@footballworld4245]

😂

[@lama6542]

you saved me

[@Arnob127]

thanks a lot :D it helped!!

[@kristakingmath]

Awesome! Thanks for letting me know.

[@asadsadsdaas3349]

is this formula works only if two planes are parallel one to another?

[@asadsadsdaas3349]

or it works in all occasions? thank you

[@Chyllandra]

I think you only can calculate the distance between planes if they are parallel because, otherwise they wil have an intersecting point somwhere - planes are infinte in 3 Dimensional space so....

[@NamweseLilain]

Hi

[@mrronolo]

A lot easier than using projections.

[@adityapatel2232]

tysm

[@omarnabil3277]

THANKS

[@kristakingmath]

+Omar nabil You're welcome!

[@Robert00000100]

Can somebody on Earth tell me how do you get 3 for 4x -6y 2z?

[@autumntruong6605]

Robert Sokolov it's initially given in the question

[@panashekabasa9235]

perfect

[@kristakingmath]

Thanks! :)

[@bright601]

almost too clear.
keep it up!

[@GODCOR]

mehn i like the way she started, and the voice... :)

[@vijaymalviya7765]

tnx mam

[@JawadAli-tj3ec]

U teach v..v.v.v.v well .....e

[@hendra6064]

Im not no