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If the volume of a parallelopiped, whose coterminus edges are given by the vectors $\vec{a} = \hat{i} + \hat{j} + n\hat{k}$, $\vec{b} = 2\hat{i} + 4\hat{j} - n\hat{k}$ and $\vec{c} = \hat{i} + n\hat{j} + 3\hat{k}$ $(n \geq 0)$, is 158 cu. units, then:
(1) $\vec{a} \cdot \vec{c} = 17$
(2) $\vec{b} \cdot \vec{c} = 10$
(3) $n = 7$
(4) $n = 9$
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