$(A)$: $\max \left\{\left|a_1\right|,\left|a_2\right|,\left|a_3\right|\right\} \leq|\vec{a}|$
$(B)$: $|\vec{a}| \leq 3 \max \left\{\left| a _1\right|,\left| a _2\right|,\left| a _3\right|\right\}$
Let $\left|a_1\right| \leq\left|a_2\right| \leq\left|a_3\right|$
$|\vec{a}|^2=\left|a_1\right|^2+\left|a_2\right|^2+\left|a_3\right|^2 \geq\left(a_3\right)^2$
$|\vec{a}| \geq\left|a_3\right|=\max \left\{\left|a_1\right|,\left|a_2\right|,\left|a_3\right|\right\}$
$A$ is true
$|\vec{a}|^2=\left| a _1\right|^2+\left| a _2\right|^2+\left| a _3\right|^2 \leq\left| a _3\right|^2+\left| a _3\right|^2+\left| a _3\right|^2$
$|\overrightarrow{ a }|^2 \leq 3\left| a _3\right|^2$
$|\overrightarrow{ a }| \leq \sqrt{3}\left| a _3\right|=\sqrt{3} \max \left\{\left| a _1\right|,\left| a _2\right|,\left| a _3\right|\right\}$
$\leq 3 \max \left\{\left| a _1\right|,\left| a _2\right|,\left| a _3\right|\right\}$
$(2)$ is true
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($A$) The function $f$ is discontinuous exactly at one point in $(0,1)$
($B$) There is exactly one point in $(0,1)$ at which the function $f$ is continuous but $NOT$ differentiable
($C$) The function $\mathrm{f}$ is $NOT$ differentiable at more than three points in $(0,1)$
($D$) The minimum value of the function $f$ is $-\frac{1}{512}$