Let $\vec a=2\hat{\imath}+\hat{\jmath}+\hat{k}$, and $\vec b,\vec c$ be two nonzero vectors such that $\left\lvert \vec a+\vec b+\vec c \right\rvert=\left\lvert \vec a+\vec b-\vec c \right\rvert$ and $\vec b\cdot\vec c=0$. Consider the statements: (A) $\left\lvert \vec a+\lambda\vec c \right\rvert \ge \lvert \vec a\rvert \text{ for all } \lambda\in\mathbb{R}$. (B) $\vec a$ and $\vec c$ are always parallel. Then,

both (A) and (B) are correct  

only (A) is correct  

 neither (A) nor (B) is correct