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

A

Only B is true

B

Only A is true

C

Both A and B are true

D

Neither A nor B is true