Question

Find T when r'(t)= (t^2, 2t, 2) for any time t

Answer 1

I got as far as \[<t^2, 2t, 2>/\sqrt(t^4+4t^2+4)\]

Answer 2

If its the unit tangent vector your want then it's
\[\frac{\vec{r}\ '(t)}{|\vec{r}\ '(t)|}\]

Answer 3

Do you know how to simplify the bottom half?

Answer 4

I don't think that's a square. But it shouldn't matter.

Answer 5

The bottom is finding the norm of r'(t), which is equivalent to \[\sqrt(x^2 + y^2 + z^2)\]

Answer 6

Yup. I meant the thing under the square root doesn't seem to be a perfect square so it's probably simplified enough

Answer 7

Ohhhhh gotcha. Haha thanks!