3. Solve the system of equations $\left\{\begin{array}{l}x^{2}+y^{2}+z^{2}=\frac{9}{4}, \\ -8 x+6 y-24 z=39 .\end{array}\right.$
3. Let vector $\vec{a}=(x, y, z), \vec{b}(-8,6,-24)$, then $\vec{a} \cdot \vec{b}=-8 x+6 y-24=39$, and $\vec{a} \cdot \vec{b}=|\vec{a}| \cdot|\vec{b}|=$ $|\vec{a}||\vec{b}| \cos \theta=26 \sqrt{x^{2}+y^{2}+z^{2}} \cos \theta=39 \cos \theta$, so, $\cos \theta=1$. Therefore, we have $x=-8 t, y=6 t, z=-24 t$, thus obtaining $x=-\frac{6}{13}, y=\frac{9}{26}, z=-\frac{18}{13}$.