Find the Unit Tangent and Unit Normal Vectors

Here we find the Unit Tangent and Unit Normal Vectors of a given vector function.

r(t) = (t^2, sint-tcost, cost + tsint)

The definitions are

T = r'/|r'|

N = T'/|T'|

When finding the unit tangent and unit normal vectors it's important to keep in mind the division by the magnitude of the derivatives.

If you're algebra is strong it should be no problem from there.