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I would like to define a real 3-D vector as, say, v = {x, y, z}, but I want it to have a fixed norm and not necessarily a unit norm. I would like to impose this condition on the vector v before I start using v in a calculation. In particular, I want Mathematica to insert x^2 + y^2 + z^2 = constant during a calculation using Solve or FullSimplify. I have used /. x^2 + y^2 + z^2 -> constant, but this simply evaluates the result for the given constant. Is there way to impose my condition before/during the calculation.

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Use == instead of = as a condition in Solve or FullSimplify. – whuber Mar 23 '13 at 7:49
up vote 3 down vote accepted

You can use the second argument of Simplify/FullSimplify to specify assumptions

v = {x, y, z};
Simplify[v.v, x^2 + y^2 + z^2 == C[0]]

or use Assuming[x^2 + y^2 + z^2 == C[0], ...].

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