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have unaligned spins, the spin vectors add up to make a vector of length ''S'' {{= 0 }} and has only one spin projection ''S''_z {{= 0}}, etc. Since baryons are made of three quarks, their spin vectors can add to make a vector of length ''S'' {{= sfrac|3|2}}}}, which has four spin projections (''S''_z {{= +sfrac|3|2}}}}, ''S''_z {{= +sfrac|1|2}}}}, ''S''_z {{= -sfrac|1|2}}}}, and ''S''_z {{= -sfrac|3|2}}}}), or a vector of length ''S'' {{= sfrac|1|2}}}} with two spin projections (''S''_z {{=

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