Finding the unit tangent vector and the unit normal vector

[@aryanroy1654]

Wow thank you so much. My teacher went over the concept of switching components to get the normal unit vector, but I was so confused on how to know the sign of the components.

[@denatyeatsnuggets7274]

THANK YOU!!! The only examples people like showing are ones where sin and cos squared becomes a constant and then I was so confused if we needed to take derivative of the magnitude too. Thank you so much ❤❤

[@ianfowler9340]

We know N(t) points toward the centre of curvature - you can see the 3/2 powers showing up. Notice that you can easily flip the componenets of T and make one negative forcing the dot product to be 0 and still maintain unit vector status. Identical result when taking negative reciprocal slopes.

[@cdkw2]

You should do a livestream some day!

[@ologhai5750]

What was the original word problem? Knowing it would make this video tastier.

[@dsx0164]

Why this parametric curves are continuous? Maybe not...

[@ianfowler9340]

For this curve: Let x^3 = 1/3t^3 and y^2 = 1/2t^2 giving us t^3 = 3x^2 and t^2 = 2y^2 a Dividing gives us: t = 3x^3/2y^2 which in turn gives y^2 = 1/2[9x^6/4y^2] = 9x^6/8y^2 Finally y^2 = +/- [3/2sqrt(2)]*x^3 ---- which is continuous everywhere. Even at the cusp (0,0).

[@phill3986]

👍😎👍

[@rootroot-pi]

why again

[@pedropiata648]

Why not