Cho ba vector \(\overrightarrow a ,\,\,\overrightarrow b ,\,\,\overrightarrow c \) thỏa mãn \(\left| {\overrightarrow a } \right| = a,\,\,\left| {\overrightarrow b } \right| = b,\,\,\left| {\overrightarrow c } \right| = c\) và \(\overrightarrow a + \overrightarrow b + 3\overrightarrow c = \overrightarrow 0 \). Tính \(A = \overrightarrow a .\overrightarrow b + \overrightarrow b .\overrightarrow c + \overrightarrow c .\overrightarrow a \)
A.\(A = {1 \over 2}\left( {{c^2} - {a^2} - {b^2}} \right)\)
B.\(A = {1 \over 2}\left( {2{c^2} - {a^2} - {b^2}} \right)\)
C.\(A = {1 \over 2}\left( {3{c^2} - {a^2} - {b^2}} \right)\)
D.\(A = {1 \over 2}\left( {3{c^2} + {a^2} - {b^2}} \right)\)