I have a line in the vector form: (x,y,z)=t(1,1,1)+(0,0,1) and I need to find a vector that represents all the points whose distance from this line equals 1. I started calculating the distance between a point (a,b,c) and this line using the vetorial product... and I got a big equation in terms of a, b and c. I think this equation describes a cylinder whose centerline is (x,y,z)=t(1,1,1)+(0,0,1). But I don't know how to get rid of this equation and obtain the vector...

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