If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are unit vectors and $\overrightarrow a+\overrightarrow b+\overrightarrow c$ is also a unit vector and $\alpha,\beta,\gamma $ are angles between $\overrightarrow a\:and\:\overrightarrow b,\:\:\overrightarrow b\:and\:\overrightarrow c\:\:\overrightarrow c\:and\:\overrightarrow a$ respectively, then among the three angles,

Question

$(a)\:All\:the\:angles\:are\:acute\:\:\qquad\:\:(b)\:\:All\:are\:rt.\:angles.\:\:\qquad\:\:(c)\:\:At\:least\:one\:is\:obtuse.\:\:\qquad\:\:(d)\:\:None\:of\:these.$