7. Given vectors $\vec{a}=\{2,3\}, \vec{b}=\{3,-2\}$, the angle between vectors $k \vec{a}+\vec{b}$ and $\vec{a}+k \vec{b}$ is $60^{\circ}$, the real number $k=$ $\qquad$
$\begin{array}{l}\text { 7. } 2 \pm \sqrt{3} \text {. } \\ k \vec{a}+\vec{b}=\{2 k+3,3 k-2\}, \vec{a}+k \vec{b}=\{2+3 k, 3-2 k\} \text {, from }(k \vec{a}+\vec{b}) \cdot(\vec{a}+k \vec{b})=| k \vec{a}+ \\ \vec{b}|\cdot| \vec{a}+k \vec{b} | \cdot \cos 60^{\circ} \text { we get } k=2 \pm \sqrt{3} \text {. }\end{array}$