The dot product of two vectors $ a = (a_1, a_2) $ and $ b = (b_1, b_2) $ is defined as:

$$ a\cdot b = a_1\cdot b_1 + a_2\cdot b_2 $$

In this case we have:

$$ \left(\dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 1 }{ 2 }\right) \cdot \left(- \dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) = \frac{\sqrt{ 3 }}{ 2 }\cdot\left(- \frac{\sqrt{ 2 }}{ 2 }\right)+\frac{ 1 }{ 2 }\cdot\left(- \frac{\sqrt{ 2 }}{ 2 }\right) = - \frac{\sqrt{ 6 }}{ 4 } + \left( - \frac{\sqrt{ 2 }}{ 4 }\right) = -0.9659 $$

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