The formula of the dot product of two vectors:
[tex] \overrightarrow{u}\circ\overrightarrow{v}=|\overrightarrow{u}|\cdot|\overrightarrow{v}|\cos\alpha [/tex]
We have:
[tex] |\overrightarrow{u}|=2\\|\overrightarrow{v}|=\dfrac{1}{9}\\\alpha=\dfrac{\pi}{4}\to\cos\dfrac{\pi}{4}=\dfrac{\sqrt2}{2} [/tex]
Substitute:
[tex] \overrightarrow{u}\circ\overrightarrow{v}=9\cdot\dfrac{1}{9}\cdot\dfrac{\sqrt2}{2}=\dfrac{\sqrt2}{2} [/tex]
