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Let a \( \in \mathrm{R} \) and the three vectors
\( \mathrm{P} \) \( \overrightarrow{\mathrm{a}}=a \hat{i}+\hat{j}+3 \hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}-a \hat{k} \) and \( \overrightarrow{\mathrm{c}}=a \hat{i}-2 \hat{j}+3 \hat{k} \).

W
Then the set \( S=\{a: \vec{a}, \vec{b} \) and \( \vec{c} \) are coplanar \( \} \)
(1) contains exactly two numbers only one of which is positive
(2) is singleton
(3) contains exaclty two positive numbers
(4) is empty
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