# unit tangent vector plz

• May 2nd 2010, 02:46 AM
falta
unit tangent vector plz
hi every one i need help

Find the unit tangent vector at the indicated point of the vector
function
r
(t) = e^15t cost i+e^15t sint j+e^15t k

T
(pi/2) =
i compute the r'(t) = (-e^15tsint+15e^15tcost)i+(e^15tcost+15e^15tsint)j+( 15te^15t)k

now i need the norm of r'(t) which i coudn't find

plz help ??!!
• May 2nd 2010, 03:02 AM
Tekken
Quote:

Originally Posted by falta
hi every one i need help

Find the unit tangent vector at the indicated point of the vector
function
r
(t) = e^15t cost i+e^15t sint j+e^15t k

T
(pi/2) =
i compute the r'(t) = (-e^15tsint+15e^15tcost)i+(e^15tcost+15e^15tsint)j+( 15te^15t)k

now i need the norm of r'(t) which i coudn't find

plz help ??!!

Forgive me if i'm wrong but isn't the unit tangent vector, $u = \frac{r'(t)}{|r'(t)|}$ Then let $t = \frac{\pi}{2}$
• May 2nd 2010, 04:01 AM
HallsofIvy
Quote:

Originally Posted by falta
hi every one i need help

Find the unit tangent vector at the indicated point of the vector
function
r
(t) = e^15t cost i+e^15t sint j+e^15t k

T
(pi/2) =
i compute the r'(t) = (-e^15tsint+15e^15tcost)i+(e^15tcost+15e^15tsint)j+( 15te^15t)k

now i need the norm of r'(t) which i coudn't find

plz help ??!!

At $t= \frac{\pi}{2}$ sin(t)= 1 and cos(t)= 0. that simplifies everything a lot!

For example, $\vec{r}(t)= e^{15\pi/2}\vec{i}+ e^{15\pi/2}\vec{k}$.
• May 2nd 2010, 08:23 AM
falta
thankx .. i got the right answer