# Vector Derivative and Tangent – Calculate a unit tangent vector to a curve in a vector presentation – Exercise 3846

Exercise

Calculate a unit tangent vector to the curve:

$$\vec{r}(t)=2\ln(t+1)\vec{i}+t^2\vec{j}+\frac{1}{2}t^2\vec{k}$$

At a point corresponding to t = 1.

$$\hat{p}=(\frac{1}{\sqrt{6}},\frac{2}{\sqrt{6}},\frac{1}{\sqrt{6}})$$