Trong không gian Oxyz, cho tứ diện ABCD với A(2; -1; 6)

Chọn D.

$\overrightarrow{BC}=\left(8;0;4\right);\overrightarrow{BD}=\left(4;3;5\right);\overrightarrow{BA}=\left(5;0;10\right)$

$\Rightarrow \overrightarrow{BD}\wedge \overrightarrow{BC}=\left(12;24;-24\right)$

$V_{ABCD}=\frac{1}{6}\left|\left(\overrightarrow{BD}\wedge \overrightarrow{BC}\right).\overrightarrow{BA}\right|=\frac{\left|5.12+0.24-10.24\right|}{6}=30$

$S_{\Delta BCD}=\frac{1}{2}\left|\overrightarrow{BD}\wedge \overrightarrow{BC}\right|=\frac{\sqrt{{12}^2+{2.24}^2}}{2}=18$

$\Rightarrow d_{\left(A,\left(BCD\right)\right)}=\frac{3V_{ABCD}}{S_{\Delta BCD}}=\frac{30.3}{18}=5$