# How can I impose a condition on Solve or FullSimplify?

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 at 7:49
You can use the second argument of Simplify/FullSimplify to specify assumptions
v = {x, y, z};

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