Cho bốn điểm \(A\left( {a;...

C

- Hướng dẫn giải

\(\begin{array}{l}\overrightarrow {BA} = \left( {a + 3;0;10} \right)\\\overrightarrow {BC} = \left( {8;0;4} \right);\overrightarrow {BD} = \left( {4;3;5} \right)\\ \Rightarrow V = \frac{1}{6}\left| {\overrightarrow {BA} \left[ {\overrightarrow {BC} ;\overrightarrow {BD} } \right]} \right|\end{array}\)

\(\begin{array}{l} = \frac{1}{6}.\left| {\left( {a + 3;0;10} \right).\left( { - 12; - 24;24} \right)} \right|\\ = \frac{1}{6}\left| { - 12\left( {a + 3} \right) + 10.24} \right| = \left| { - 2a + 34} \right|\\V = 30 \Leftrightarrow a = 2;a = 32\end{array}\)