Question

find the unit tangent vector to the curve r(t)=((t^-1)+t),((t^-1)+t),-1) at t=1

Answer 1

Find \(\mathbf{r}'(t)\)
Can you do it?

Answer 2

The Unit Tangent Vector is, obviously, a unit vector and it is defined as:
\[=\frac{ r \prime (t) }{ \left| r \prime (t) \right| }\]

Answer 3

\(\mathbf{r}'(t)\) is the tangent vector. To make it unit, divide by magnitude \[
\mathbf{\tau}(t) = \frac{\mathbf{r}'(t)}{\|\mathbf{r}'(t)\|}
\]

Answer 4

ok thanks i think i can do this now