Let $$\triangle PQR$$ be a triangle. Let $$\overrightarrow{a} = \overrightarrow{QR}, \overrightarrow{b} = \overrightarrow{RP}$$ and $$\overrightarrow{c} = \overrightarrow{PQ}$$. If $$|\overrightarrow{a}| = 12, |\overrightarrow{b}| = 4 \sqrt 3$$ and $$\overrightarrow{b}. \overrightarrow{c}$$ then which of the following is (are) true?

A

$$\frac{|\overrightarrow{c}|^2}{2} - |\overrightarrow{a}| = 12 $$

B

$$\frac{|\overrightarrow{c}|^2}{2} + |\overrightarrow{a}| = 30 $$

C

$$|\overrightarrow{a} \times \overrightarrow{b} + \overrightarrow{c} \times \overrightarrow{a}| = 48 \sqrt 3$$

D

$$\overrightarrow{a} . \overrightarrow{b} = -72$$