Free Version
Easy

# Unit Tangent Vector

MVCALC-O0XKQE

Find the unit tangent vector $\vec{T}(t)$ to the graph of the vector function:

$$\vec{r}(t)=(3\sin t)\vec{i} + (t)\vec{j} - (3\cos t)\vec{k}$$

A

$\vec{T}(t)=(3\sin t)\vec{i} - \vec{j} + (3\cos t)\vec{k}$

B

$\vec{T}(t)=(3\cos t)\vec{i} + \vec{j} + (3\sin t)\vec{k}$

C

$\vec{T}(t)=(3\sin t)\vec{i} - \vec{j} - (3\sin t)\vec{k}$

D

$\vec{T}(t)=(\frac{3}{\sqrt{10}}\cos t)\vec{i} + (\frac{1}{\sqrt{10}})\vec{j} + (\frac{3}{\sqrt{10}}\sin t)\vec{k}$

E

$\vec{T}(t)=(\frac{3}{\sqrt{10}}\cos t)\vec{i} - (\frac{1}{\sqrt{10}})\vec{j} + (\frac{3}{\sqrt{10}}\sin t)\vec{k}$