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If $\frac{\pi}{2} < \theta \leq$ and $|\overline{\mathrm{a}}|=5,|\overline{\mathrm{b}}|=13,|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=25$, then the value of $\bar{a} \cdot \bar{b}$ is
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-60
$\begin{aligned} & |\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=25 \\ & \therefore|\overline{\mathrm{a}}| \cdot|\overline{\mathrm{b}}| \cdot \sin \theta=(5)(13) \sin \theta=25 \\ & \therefore \sin \theta=\frac{5}{13} \Rightarrow \cos \theta=\frac{-12}{13} \\ & \overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=|\overline{\mathrm{a}}| \cdot|\overline{\mathrm{b}}| \cdot \cos \theta \\ & =(5)(13)\left(\frac{-12}{13}\right)=-60\end{aligned}$
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