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# How to turn into vector units?

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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 :)

math
Aug 20, 2014

#2
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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

= cos(t)i + j - sin(t)k

Aug 20, 2014

#1
+5

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.   Aug 20, 2014
#2
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