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**pakman** Let $\displaystyle \vec{x}$ and $\displaystyle \vec{y}$ be linearly independent vectors in $\displaystyle R^2$. If ||$\displaystyle \vec{x}$|| = 2 and ||[$\displaystyle \vec{y}$|| = 3, what, if anything, can we conclude about the possible values of |**$\displaystyle \vec{x}^{T}\vec{y}$**|?

So this is what I have so far...

$\displaystyle 2 = \sqrt{x_{1}^{2}+x_{2}^{2}}$

$\displaystyle 3 = \sqrt{y_{1}^{2}+y_{2}^{2}}$

After some algebra I got...

$\displaystyle \vec{x}^{T}\vec{y}=(\sqrt{4-x_{2}^{2}}\sqrt{4-x_{1}^{2}})(\sqrt{9-y_{2}^{2}}\sqrt{9-y_{1}^{2}})^{T}$

This is where I'm stuck, what can I determine from this? Thanks in advance!