For any vector $\vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k}$, with $10\left|a_{i}\right|

Question

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 :

(A): $\max \left\{\left|a_{1}\right|,\left|a_{2}\right|,\left|a_{3}\right|\right\} \leq|\vec{a}|$

(B) : $|\vec{a}| \leq 3 \max \left\{\left|a_{1}\right|,\left|a_{2}\right|,\left|a_{3}\right|\right\}$

Only (B) is true

Only (A) is true

Neither (A) nor (B) is true

Both (A) and (B) are true

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