Question

Find u · v, where is the angle between u and v.
||u||=25 ||v||=400 =3pi/4

Answer 1

`~~~~~~~~~~~~\textit{angle between two vectors } \\\\ \cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\underset{\textit{magnitude product}}} \implies \measuredangle \theta = \cos^(-1)\left(\cfrac{u \cdot v}~\right) \\\\[-0.35em] ~\dotfill`

`\cfrac{3\pi }{4}=\cfrac{u\cdot v}\implies \cfrac{3\pi }{4}=\cfrac{u\cdot v}{25\cdot 400}\implies \cfrac{3\pi }{4}=\cfrac{u\cdot v}{1000} \\\\\\ \cfrac{(3\pi )(1000)}{4}=u\cdot v\implies 750\pi =u\cdot v`