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January 28th, 2012, 10:43 AM   #1
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Vector \ Three dimensional Space Question

let be a fixed vector. Describe the set of all vectors such that

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?
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January 28th, 2012, 11:34 AM   #2
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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
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January 28th, 2012, 11:53 AM   #3
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Re: Vector \ Three dimensional Space Question

The set is that of all vectors such that the vector has modulus 1.

Clearly you'll have a set of equidistant points in space with the same origin which will vary the direction when choosing an appropiate , but as all vectors will have the same length, they'll describe a sphere with radius 1 and center at
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