First, we need to find the dot product of the two vectors $\overrightarrow{\mathbf{A}}$ and $\overrightarrow{\mathbf{B}}$:
$\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}} = (-3)(6) + (7)(-10) + (-4)(9) = -18 - 70 - 36 = -124$
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