If:

x=sin(t)

y=t+1

z=cos(t)

the derivative of each are:

dx/dt=cos(t)

dy/dt=1

dz/dt=-sin(t)

how do I convert it into unit vectors (ie i,j,k)

the t is time.

Thanks Again guys :)

Oli96
Aug 20, 2014

#1**+5 **

A three space unit vector is defined as <v_{1 }/ llvll , v_{2 }/ llvll , v_{3 }/ 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.

CPhill
Aug 20, 2014