normal and osculating planes (KristaKingMath)

► My Vectors course: www.kristaking...
In this video we'll learn how to find the equations of the normal and osculating planes of a parametric equation.
● ● ● GET EXTRA HELP ● ● ●
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...
FACEBOOK // / kristakingmath
TWITTER // / kristakingmath
INSTAGRAM // / kristakingmath
PINTEREST // / kristakingmath
GOOGLE+ // plus.google.co...
QUORA // www.quora.com/...

[@wendys444.]

Rarely do I comment on things, but this video was perfectly laid out. I watched this an hour before my quiz and I remembered everything. Thank you!

[@kristakingmath]

You’re so welcome! And I’m so glad it helped on the quiz!! 🫶

[@ZDanimations]

the normal vector equation should be y=6x+pi, just a tiny sign error

[@raymondimpara9016]

I spent almost an hour trying to find an explanation for this type of problem, including my calculus book, and this is the best explanation/example by far

[@kristakingmath]

+RAymond Impara Thank you so much, I'm glad it helped!

[@ilealow9951]

In just the first 2 min I finally understood how to find the normal and osculating equations. Thank you!!

[@meamor123456789]

I still don't get why we use the coefficients of r'(t) to find our normal plane equation. My instinct would say to use the coefficients of N(t) (the same way we use the coefficients of B(t) to find the equation of the osculating plane). Help? :(

[@mariorodin9246]

Thank you so much! This helped me immensely on my Calc 3 homework.

[@starRushi]

Lifesaver, actual lifesaver. Taking a fully online, non-interactive course. You've single-handedly returned my sanity and for that, I thank you, so much.

[@kristakingmath]

I'm so glad I was able to help! I know online courses can be really tough when you're trying to get through all the material completely by yourself. :)

[@certifiedsmartass4122]

@@kristakingmath Why haven't you posted in a while?

[@jakallslsosasdghjkl6558]

Thank you! I have a test in 45 minutes and this was a real lifesaver :))) I've been so confused because I kept thinking that for the normal plane you would need to use the normal vector (I mean it makes sense lol) but this clarified everything for me!

[@kristakingmath]

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

[@noellemarievillanueva5835]

Why is r'(t) being evaluated at t=pi as the normal vector on the normal plane and not N(t)? Because I recall you saying at the beginning that N(t) lies within the normal plane, so we'd have to take its components to plug in for a, b and c.

[@diagotorres4094]

+Noelle Marie Villanueva , I think! its because a plane is described using a normal vector, so the normal vector of the NORMAL plane would be the equivalent of the tangent of the curve, or r`(t). The N(t) does not describe the plane, its just a vector that lies within the plane. Remember a normal vector is just an orthogonal/perpendicular vector. She could have used T(t), and get the same equation with just scaled co-efficents.

[@user-gl8hf6ts8t]

Powerful work,it has greatly helped me

[@sfadhjkl4112]

FYI "osculating" is not the same as "oscillating," you were saying "oscillating."

[@pspuser1100]

agreed

[@quantstyle6448]

You did a remarkable job:)

[@LeRationalRabbit]

Not to pick nits but the pronunciation is \ˈäs-kyə-ˌlāt\. The 'c' is a hard c.

[@sgedeon01]

Shouldn't the equation of the normal plane be y=6x+pi since you are solving for y when you have -6x+y-pi=0?

[@Gismho]

Excellent explanation. Thank you so much for clear and concise procedure.

[@kristakingmath]

You're welcome, Les, I'm so glad it made sense! :)

[@user-qo8hd6jk6i]

That curve is not unit speed curve. How are you using Frenet-Serret for unit speed curves?

[@MasterChiefCovenant]

thank you for your great videos on calc 2

[@jferro96]

thank you so much. you helped me out a lot

[@kristakingmath]

+J Ferro You're welcome, I'm glad I could help!

[@Thomas-bs2em]

I would give you two thumbs up if I could Krista, you are a Great Teacher! but graphing out the formulas in Geogebra 3d it looks like for the Normal Plane y = 6x+pi.

[@_towards_destination]

Thank you soo muchhh 🤗🤗🤗 I got every single question's answer regarding this topic.. Welldone and keep it up!

[@kristakingmath]

Thanks, Maths! I'm glad it helped! :)

[@btcbtc3129]

Thank you for the video, It really helps a lot

[@kristakingmath]

Yay! Thanks for letting me know.

[@rishabhnegi479]

Thank you so much for the help 🤗🤗🤗🤗🤗😇😇😇🤖🤖

[@borjalarrain6335]

Why do you use the values of r'(pi) for a,b,c instead of the values of the normal_vector(pi)?

[@moldirkenzhekulova]

WOW! Thanks a lot! It's very easy and clear to undestand!

[@kristakingmath]

+Moldir Kenzhekulova So glad I could help!

[@ethanrottenberger2967]

For the osculating plane, don't you have to distribute the 1/sqrt37 to a, b, and c?

[@a.morales332]

Thank you!!

[@encycolopediadiversa319]

This is the same question which was asked in our midsems at bits pilani, india. Can you tell me from which book you have taken this question

[@prabhurout6078]

Amazing

[@wetbadger2174]

My y = 12t. How do I proceed?

[@WalkerFlexasRanger]

Excellent video, excellent explanation. Thank you!

[@kristakingmath]

You're welcome, thank you so much!

[@jvstbreathe]

You saved me! Bless.

[@michaelgibbons7014]

Amazing job! Perfect presentation.

[@kristakingmath]

+Michael Gibbons Thank you so much!

[@AcidLake99734]

For the normal plane: it should be y=6x+Pi.

[@kristakingmath]

Good catch, thanks! I've added an annotation to clear up any confusion.

[@vmguptajr]

Y=6X+π and not -π in the final normal equation

[@amiteshchoudhary2275]

Thanku mama

[@cameroncrowe7825]

Helped so much!

[@mudasirjan06]

Since 10th grade I have been finding your solutions to my hw problems. Im now second year of attaining my degree and still here. How time moves by 😢

[@kristakingmath]

Wow that’s awesome!! Congrats on working toward finishing your degree, I’m so happy for you!! ❤️☺️

[@stevekhan4063]

i have a curious question, does calc 3 get any messier than this ? lol

[@cykoshadow]

yes

[@katlegophiri-primary8176]

Thank you 😄

[@sasithrennathan795]

How to find equation of rectifying plane?

[@keishlamvera-martinez9853]

thank you so much for this! a lifesaver!

[@kristakingmath]

So glad it helped!

[@javiermendez1018]

Oh no... 15:45 she forgot to make the sign in front of 6sin(3t) positive because they cancel out, and she goes forward with that later on.

[@chesterisaacs1502]

you are the baaaaas!!(that's boss! in Afrikaans)

[@KhabisangLekena]

Well presented

[@kristakingmath]

Khabisang Lekena Thanks!

[@forheuristiclifeksh7836]

1:00

[@jeremylodge2235]

What if you were just given t=pi

[@imaculadaboavida8092]

wow,,you are so smart,,,

[@kwasifahie2513]

what program do you use?

[@kristakingmath]

+Kwasi Fahie kristakingmath (dot) com / my-videos

[@Coggernautt]

You have saved me from failing! THANK YOU!

[@kristakingmath]

I'm glad I can help along the way! 😊

[@imeredithc]

Thank you! You made this very easy to understand!

[@kristakingmath]

I'm so glad I could help!

[@kora2511]

thank u mam

[@Coppah]

you a G

[@Creoleitalian]

Y= 6x+pi.

[@marcelgunadi2429]

cross product is wrong

[@andrewmuller552]

Kick ass

[@howardwolowitz762]

I love u, lol.

[@aiadaali139]

ذكتور نريد التواصل معكم على الخاص

[@ZDanimations]

disregard last comment, im on a phone so i didnt know there were annotations whoops

[@murkalurk]

Why even bother finding N(t)?

[@LYNXzTwist]

The osculating plane is the plane spanned by n and t

[@michaelhan4266]

Since the osculating plane is perpendicular to B(t), you need to first find B=TxN, then use B to find the osculating plane.

[@mariorodin9246]

Jesus is LORD!

[@certifiedsmartass4122]

Bruh

[@lambda5949]

not funny didn't laugh