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Let \[\alpha \in R\] and the three vectors \[\overset{\to }{\mathop{a}}\,=\alpha \hat{i}+\hat{j}+3\hat{k},\] \[\overset{\to }{\mathop{b}}\,=2\hat{i}+\hat{j}-\alpha \hat{k}\] and \[\overset{\to }{\mathop{c}}\,=\alpha \hat{i}-2\hat{j}+3\hat{k}.\]  Then, the number of elements in the set S=( \[\alpha :\overset{\to }{\mathop{a}}\,,\,\,\vec{b}\] and \[\overset{\to }{\mathop{c}}\,\] are coplanar) is

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