Given two distinct nonzero vectors $v_1 and v_2$ in 3 dimensions, define a sequence of vectors by  
$v_{n+2}=v_n\times v_{n+1}(so{v}_3=v_1\times v_2,v_4=v_2\times v_{3}andsoon)$  $LetS=\{v_n/n=1,2,\mathrm{.....}\}andU=\{\frac{v_n}{\left|v_n\right|}/n=1,2,\mathrm{.....}\}.$ 
(Note: Here $\times$ denotes the cross product of vectors and $\left|v\right|$ denotes the magnitude of the vector v. The vector 0 with 0 magnitude, if it occurs in S, is counted. But in that case of course the 0 vector is not considered while listing elements of U. number of elements in set  S is called cardinality of  S) 
$S_1:$ There exist vectors $v_{1}and{v}_2$ for which the cardinality of S is 2.
$S_2:$ There exist vectors $v_{1}and{v}_2$ for which the cardinality of S is 3.
$S_3:$ There exist vectors $v_{1}and{v}_2$ for which the cardinality of S is 4.
$S_4:$  Suppose that for some $v_{1}and{v}_2$, the set S is infinite then the set U is also infinite.
The number of TRUE statements among the $S_1,S_2,S_3,S_4$ is