# Thread: Finding unit tangent vectors

1. ## Finding unit tangent vectors

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?

2. ## Re: Finding unit tangent vectors

If r(t) is the position vector, then the unit tangent vector is $\frac{r&#39;(t)}{||r&#39;(t)||}$.

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