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 January 28th, 2012, 10:43 AM #1 Senior Member   Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0 Vector \ Three dimensional Space Question let $\vec{r_0}$ be a fixed vector. Describe the set of all vectors $\vec{r}$ such that $|\vec{r}-\vec{r_0}|=1$ This is from the vector section in our book. I can not get very far with this question. We just covered three-dimensional space, so I think they mean vectors in three-dimensions. Any Ideas?
 January 28th, 2012, 11:34 AM #2 Member   Joined: Aug 2010 Posts: 49 Thanks: 0 Re: Vector \ Three dimensional Space Question Hi, if you are talking about 3D it is describing a sphere of radius 1. Best regards, Jens PS: With the center of the sphere in $\vec{r_0}$
 January 28th, 2012, 11:53 AM #3 Senior Member   Joined: Dec 2011 From: Argentina Posts: 216 Thanks: 0 Re: Vector \ Three dimensional Space Question The set is that of all vectors $r$ such that the vector ${r-r_0}$ has modulus 1. Clearly you'll have a set of equidistant points in space with the same origin $r_o$ which will vary the direction when choosing an appropiate $r$, but as all vectors will have the same length, they'll describe a sphere with radius 1 and center at $r_0= (x,y, z)$

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