normal and osculating planes (KristaKingMath)

In this video we'll learn how to find the equations of the normal and osculating planes of a parametric equation.

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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?!”

[wendys.]

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!

[ZDanimations]

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

[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.

[ilealow]

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

[noellemarievillanueva]

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.

[raymondimpara]

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

[mariorodin]

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

[jakallslsosasdghjkl]

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!

[meamor]

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? :(

[sfadhjkl]

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

[FelixNDHLOVU]

Powerful work, it has greatly helped me

[Gismho]

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

[sgedeon]

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?

[borjalarrain]

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

[LeRationalRabbit]

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

[encycolopediadiversa]

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

[_towards_destination]

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

[ethanrottenberger]

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

[재훈장-rn]

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

[Thomas-bsem]

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.