Cho 4 điểm \(A\,(1;1;0);\,\,B\,(0;2;1);\,\,C\,(1;0...

B

- Hướng dẫn giải

Ta có: \(\overrightarrow{AB}=(-1;1;0);\,\,\overrightarrow{AC}=(0;-1;2);\,\,\overrightarrow{AD}=(0;0;1)\)

Thể tích tứ diện ABCD là:

\({{V}_{ABCD}}=\frac{1}{6}\left| \left[ \overrightarrow{AB},\overrightarrow{AC} \right].\overrightarrow{AD} \right|=\frac{1}{6}.\)

\({{S}_{\Delta BCD}}=\frac{1}{2}\left| \left[ \overrightarrow{BC},\overrightarrow{BD} \right] \right|=\frac{\sqrt{3}}{2}.\)

\({{h}_{A}}=\frac{3V}{{{S}_{BCD}}}=\frac{\sqrt{3}}{3}\)