Chọn B
Ta có:
\(\frac{7}{3} \left|z+4i\right|+\left|z-6i\right|\ge \frac{10}{3} \left|z+i\right| \)
\(\frac{7}{3} \left|z-6i\right|+\left|z+4i\right|\ge \frac{10}{3} \left|z-3i\right|\)
\(\Rightarrow \left|z+4i\right|+\left|z-6i\right|\ge \left|z+i\right|+\left|z-3i\right|\)
Mà \(\left|z+4i\right|+\left|z-6i\right|=\left|z+i\right|+\left|z-3i\right| \)
\(\Rightarrow \left\{\begin{array}{c} {\left[\begin{array}{c} {z-6i=0} \\ {\frac{7}{3} z+\frac{28}{3} i=k\left(z-6i\right)\, \, \, \, \left(k\ge 0\right)} \end{array}\right. } \\ {\left[\begin{array}{l} {z+4i=0} \\ {\frac{7}{3} z-\frac{42}{3} i=k\left(z+4i\right)\, \, \, \, \, \left(k\ge 0\right)} \end{array}\right. } \end{array}\right. \)
\(\Rightarrow M\in Oy\, \, \, \, \left(y\le -4,\, \, y\ge 6\right) \) mà \(\left|z\right|\le 10\)
\(\Rightarrow \left[\begin{array}{l} {M\in Oy,\, \, -10\le y\le -4} \\ {M\in Oy,\, \, \, 6\le y\le 10} \end{array}\right. \)
Vậy có 5+7=12 điểm.