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Let $A$ be a point on the line $\vec{r} = (1 - 3\mu)\hat{i} + (\mu - 1)\hat{j} + (2 + 5\mu)\hat{k}$ and $B(3, 2, 6)$ be a point in the space. Then the value of $\mu$ for which the vector $\overrightarrow{AB}$ is parallel to the plane $x - 4y + 3z = 1$ is:
(1) $\frac{1}{4}$
(2) $\frac{1}{8}$
(3) $\frac{1}{2}$
(4) $\frac{1}{4}$
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