Let $$\vec{a}$$, $$\vec{b}$$, $$\vec{c}$$ be three vectors mutually perpendicular to each other and have same magnitude. If a vector $$\vec{r}$$ satisfies $$\vec{a} \times \{\vec{r} - \vec{b} \times \vec{a}\} + \vec{b} \times \{\vec{r} - \vec{c} \times \vec{b}\} + \vec{c} \times \{\vec{r} - \vec{a} \times \vec{c}\} = \vec{0}$$, then $$\vec{r}$$ is equal to:

A

$$\frac{1}{3}(\vec{a} + \vec{b} + \vec{c})$$

B

$$\frac{1}{3}(2\vec{a} + \vec{b} - \vec{c})$$

C

$$\frac{1}{2}(\vec{a} + \vec{b} + \vec{c})$$

D

$$\frac{1}{2}(\vec{a} + \vec{b} + 2\vec{c})$$