How to turn into vector units?

I wonder if this is asking about how to express the position and velocity in terms of the unit vectors, i, j and k.

If so, then, using p for position and v for velocity:

p = sin(t)i + (t+1)j + cos(t)k

v = cos(t)i + j - sin(t)k

A three space unit vector is defined as <v₁ / llvll , v₂ / llvll , v₃ / llvll >  where v1, v2, v3 are the individual components  of a given vector, v, and llvll is the length of that vector.

So we have 

v = <sin(t) , t + 1 , cos(t) >      And llvll = √ (sin(t)² + (t + 1)² + (cos(t)² ) = √( t2 + 2t + 2)

So, our unit vector is  < sin(t) /  √( t2 + 2t + 2), (t + 1) / √( t2 + 2t + 2), cos(t) / √( t2 + 2t + 2) >

The same procedure could be used to find the length of the derivative vector.