Finding unit tangent vectors

jwpaine

Full Member
Joined
Mar 10, 2007
Messages
723
The web homework is not accepting my answer for this, even though I've done it like the others. Have I made a mistake?

given r(t) = (t^2, t^3), find the unit tangent vector at T(t) at t = 1:

r(t) = t^2i + t^3j

T(t) = (t^2i + t^3j) / sqrt ( t^4 + t^6)
T(1) = ( i + j) / sqrt(2)

Thus: T(1) = <sqrt(2)/2 , sqrt(2)/2>

Yes, no?
 
If r(t) is the position vector, then the unit tangent vector is \(\displaystyle \frac{r'(t)}{||r'(t)||}\).
 
Top