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How can I plot the vector function $r(t) = i + j + t\;k$, where i, j, k are unit vectors, and t is the parameter of the function r.

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you want the vector field or just the vector bundle? – Spawn1701D Apr 11 '13 at 22:44
belisarus answered my question. thank you. – MathStudent Apr 11 '13 at 22:49
And you really couldn't find this in the documentation? – Sjoerd C. de Vries Apr 11 '13 at 22:50
@MathStudent you are welcomed. – Spawn1701D Apr 11 '13 at 22:54
up vote 4 down vote accepted
ParametricPlot3D[{1, 1, t}, {t, 0, 2}]

enter image description here

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thank you, belisarius. you saved my life. – MathStudent Apr 11 '13 at 22:49
@MathStudent No, I just answered a very simple question. I suggest you to read a few coding examples in the Help system. – Dr. belisarius Apr 11 '13 at 23:10
... if you want to live safe – Dr. belisarius Apr 12 '13 at 11:33
Hmm... That's not really the graph of the requested function but rather the image of the function (over an interval of the domain, of course). To plot the actual function would be to plot a function from (some subinterval) of the reals R to 3-space [latex]R^3[/latex], and that would require working in 4-space; or it would require creating an animation or dynamic display in which the domain is represented by time. – murray Apr 12 '13 at 12:37
@murray Yep, but it is the only thing that I was able to produce in **R**^3 – Dr. belisarius Apr 12 '13 at 12:41

Even though belisarius has answered the question to OP's satisfaction, I figured I'd throw this in there in case someone came to this question looking to plot a vector field in three dimensions like murray suggested.

   VectorPlot3D[{1, 1, t}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1},          
   VectorScale -> Medium, RegionFunction -> ((#1 #2 #3 > 0) &)],      
{t, 0, 2}]  

Information about the options I applied (to make the plot look a bit easier to understand) is in the documentation for VectorPlot3D.

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