Answer
$12500\sqrt 3$
Work Step by Step
We know that the angle between two vectors is:
$\theta =\cos^{-1} [ \dfrac{u \cdot v}{||u|| \space ||v|| }]$
Therefore, $\cos (\dfrac{\pi}{6}) = \dfrac{u \cdot v}{(100)(250) }$
or, $u \cdot v= 25,000 \times (\dfrac{\sqrt 3}{2})$
or, $u \cdot v=12500\sqrt 3$
