How to maximize this function

We are in an euclidian space, and we have to maximize the quadratic form : $x\in B\rightarrow (x|u) (x|v)$where $u$ and $v$ are two given vectors, and $B=\{x:||x||\leq1\}$

I don't find where i have to begin...

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What does $x|u$ even mean? –  5xum Jul 3 '14 at 11:05
The dot product of $x$ and $u$ (in France, we use sometimes this notation). –  D.L. Jul 3 '14 at 11:06

Sorry, i have finally found the answer. It becomes easy if you use the orthogonal projection $p(x)$ of $x$ on $Vect(u,v)$. Then it is one bidimensional problem.