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**Q:Given non-zero vectors u and v, find a vector x such that both equalitites x dot u=|u|, and x cross u = v hold. What should be the mutual position of the given vectors u and v in space, so that the problem has a solution?**

What I've got so far:

Setting x = au + b(u cross v)

I have that

a=1/|u| and b= +/- |v| / |u cross (u cross v)|

This answers the first part of the question, but I don't get the second part (i.e. What should be the mutual position of the given vectors u and v in space, so that the problem has a solution?)

Thanks for helping and explaining!