Answer
$\mathbf{u}\cdot\mathbf{v}=-500\sqrt{3}$
Work Step by Step
$\mathbf{u}\cdot\mathbf{v}=\|\mathbf{u}\|\|\mathbf{v}\|\cos{\theta}$
$\|\mathbf{u}\|=40$
$\|\mathbf{v}\|=25$
$\cos{\theta}=\cos{\frac{5\pi}{6}}=-\frac{\sqrt{3}}{2}$
therefore,
$\mathbf{u}\cdot\mathbf{v}=40\times25\times\left(-\frac{\sqrt{3}}{2}\right)=-500\sqrt{3}$
