For any vector $\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}$, with $10\left|a_i\right|<1, i=1,2,3$, consider the following statements $(\mathrm{A}): \max \left\{\left|\mathrm{a}_1\right|,\left|\mathrm{a}_2\right|,\left|\mathrm{a}_3\right|\right\} \leq|\overrightarrow{\mathrm{a}}|$ $(\mathrm{B}):|\overrightarrow{\mathrm{a}}| \leq 3 \max \left\{\left|\mathrm{a}_1\right|,\left|\mathrm{a}_2\right|,\left|\mathrm{a}_3\right|\right\}$