Let $$\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$$ be unit vectors such that $$\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = \overrightarrow{0}$$. Which one of the following is correct?

$$\overrightarrow{a} \times \overrightarrow{b} = \overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{c} \times \overrightarrow{a} = \overrightarrow{0}$$

$$\overrightarrow{a} \times \overrightarrow{b} = \overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{c} \times \overrightarrow{a} \neq \overrightarrow{0}$$

$$\overrightarrow{a} \times \overrightarrow{b} = \overrightarrow{b} \times \overrightarrow{c} = \overrightarrow{a} \times \overrightarrow{c} \neq \overrightarrow{0}$$

$$\overrightarrow{a} \times \overrightarrow{b}, \overrightarrow{b} \times \overrightarrow{c}, \overrightarrow{c} \times \overrightarrow{a}$$ are mutually perpendicular