For any vector vec{a} = a_1 hat{i} + a_2 hat{ | vedclass

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(D) Without loss of generality,let $|a_1| \leq |a_2| \leq |a_3|$.For statement $(A)$:$|\vec{a}|^2 = |a_1|^2 + |a_2|^2 + |a_3|^2 \geq |a_3|^2$.Taking t

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Both $(A)$ and $(B)$ are true

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(D) Without loss of generality,let $|a_1| \leq |a_2| \leq |a_3|$.For statement $(A)$:$|\vec{a}|^2 = |a_1|^2 + |a_2|^2 + |a_3|^2 \geq |a_3|^2$.Taking the square root,$|\vec{a}| \geq |a_3| = \max \{|a_1|, |a_2|, |a_3|\}$.Thus,$(A)$ is true.For statement $(B)$:$|\vec{a}|^2 = |a_1|^2 + |a_2|^2 + |a_3|^2 \leq |a_3|^2 + |a_3|^2 + |a_3|^2 = 3|a_3|^2$.Taking the square root,$|\vec{a}| \leq \sqrt{3} |a_3| = \sqrt{3} \max \{|a_1|, |a_2|, |a_3|\}$.Since $\sqrt{3} Thus,$(B)$ is also true.Therefore,both $(A)$ and $(B)$ are true.

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:
$(A): \max \{|a_1|, |a_2|, |a_3|\} \leq |\vec{a}|$
$(B): |\vec{a}| \leq 3 \max \{|a_1|, |a_2|, |a_3|\}$

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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|\}$