\textbf{141.} Vector $\vec{a} = (-1, \alpha, 1)$ makes a $45°$ angle with the $z$-axis in space. If $\vec{b} = \left(-\dfrac{4}{3}, \dfrac{2}{3}, 2\right)$ and the angle of vector $\vec{a} \times \vec{b}$ with the $z$-axis is $\theta$, then $\cos\theta$ is which of the following?
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(1) $-\dfrac{\sqrt{3}}{3}$ \hfill (2) $-\dfrac{\sqrt{3}}{4}$ \hfill (3) $\dfrac{\sqrt{3}}{4}$ \hfill (4) $\dfrac{\sqrt{3}}{2}$
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