Let A and B denote the statements A: $\cos \alpha + \cos \beta + \cos \gamma = 0$ B: $\sin \alpha + \sin \beta + \sin \gamma = 0$ If $\cos \left( {\beta - \gamma } \right) + \cos \left( {\gamma - \alpha } \right) + \cos \left( {\alpha - \beta } \right) = - {3 \over 2},$ then:

Question

Let A and B denote the statements

A: $\cos \alpha + \cos \beta + \cos \gamma = 0$

B: $\sin \alpha + \sin \beta + \sin \gamma = 0$

If $\cos \left( {\beta - \gamma } \right) + \cos \left( {\gamma - \alpha } \right) + \cos \left( {\alpha - \beta } \right) = - {3 \over 2},$ then:

A is false and B is true

both A and B are true

both A and B are false

A is true and B is false

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