# Thread: Calculus III unit tangent and unit normal vectors

1. ## Calculus III unit tangent and unit normal vectors

Consider the following vector function: r(t) = {2t*sqrt(2),e^2t,e^-2t}.

(a) Find the unit tangent and unit normal vectors T(t) and N(t).

(b) Finding the curvature (k(t).

Thanks!

2. ## Re: Calculus III unit tangent and unit normal vectors

Originally Posted by jessie546311
Consider the following vector function: r(t) = {2t*sqrt(2),e^2t,e^-2t}.
(a) Find the unit tangent and unit normal vectors T(t) and N(t).

(b) Finding the curvature (k(t).

$T=\frac{R'}{\|R'\|}$, $N=\frac{T'}{\|T'\|}=\frac{R\times(R''\times R')}{\|R\times(R''\times R')\|}$

$\kappa(t)=\frac{R'\times R''}{\|R'\|^3}$