Introduction to unit tangent, unit normal, and unit binormal vectors (Calculus 3 basics)

Here's a quick introduction to unit tangent, unit normal, and unit binormal vectors that you need to know for your Calculus 3 class! Subscribe to ‪@bprpcalculusbasics‬ for more calculus tutorials!
Proof that if a vector has constant length, then it's orthogonal to r': • If a vector has consta...
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[@buddermybacon2805]

Super cool that you’re doing calc III videos now. Very interesting and well explained as always 💯

[@bprpcalculusbasics]

Thank you!

[@MrKoteha]

Calculus 3 videos are very interesting! Can't wait for the next one

[@bprpcalculusbasics]

Glad you like them!

[@paradox6647]

Loving this new series, please keep it up

[@TroyBurgess-l2r]

Appreciate your help! Truly grateful!

[@bprpcalculusbasics]

Happy to help!

[@perekman3570]

I feel that the calc3 videos are in the wrong order somehow. For example, the Unit Tangent Vector has been mentioned i several videos already, but isn't explained until now. But the explanation is excellent, as per usual.

[@ianfowler9340]

Very, very nice presentation. So, ( apologies if I am spoiling your next video ) .....where, exactly, is vector N pointing?? - toward a very special point. Your current and recent videoes have already given us the answer. It is staring right at us.

[@bprpcalculusbasics]

You mean N is pointing at the center of curvature, right? 😃

[@ianfowler9340]

@@bprpcalculusbasics Bang on!! So now break up the acceleration vector, R ' '(t) , into 2 rectangular componenets (not a_x and a_y) : instead, one in the direction of the tangent (a_t) and perpendicular to the tangent (a_n). This normal component point of acceleration, a_n, points right at the Center of Curvature. And if a point mass is moving along the curve, it's the a_n component of the accelaeration that makes it turn, whereas a_t increases or decreases the speed = |vector v|. So cool. Thanks, yet again, for another great video - Newton is smiling.

[@bprpcalculusbasics]

@@ianfowler9340 yes. I actually just did that video two days ago! And you can probably guess what comes after that! Btw, I am following the calc book by Thomas and I think it’s a fantastic book.

[@charlesspringer4709]

Differential Geometry is the coolest! Well, coolest except for Clifford Algebra and Geometric Calculus :-)

[@ruud9767]

Deetee deeree! T! Deetee? Plus N! TNT. Boom!

[@brycenbg9372]

Blind person be like: Why there are so many dt 😂 😂

[@cyrusyeung8096]

Nice video. But please stop saying divide by dt (as in 1:53). It is not how derivative works.

[@ianfowler9340]

I hear your frustration. But differentials are defined in such a way so as to force
"the operation: [d by dx][of y]" to actually equal "the division: (differential of y)/(diffrerential of x)".
That is, to force "dy by dx" to behave like a fraction - at least for mult. and division. There are no restrictions on the size of the diff. of x (or dx) - large or as small as you want, because:
dx is defined as delta x and
dy is defined as f '(x)*delta x = f '(x)dx. Re-arranging we obtain: "(diff. of y) divided by (diff. of x)" is indeed equal to f ' (x).

[@samuraijosh1595]

Dang why did this one fail so badly? The algorithm did you dirty

[@perekman3570]

It will remain useful for students for years to come.