Cho bốn điểm \(A(a;-1;6),B(-3;-1;-4). C(5;-1;0), D...

C

- Hướng dẫn giải

Ta có:

\(\begin{array}{l} \overrightarrow {BA} = \left( {a + 3;0;10} \right),\overrightarrow {BC} = \left( {8;0;4} \right);\overrightarrow {BD} = \left( {4;3;5} \right)\\ \Rightarrow \left[ {\overrightarrow {BC} ,\overrightarrow {BD} } \right] = \left( { - 12; - 24;24} \right)\\ {V_{ABCD}} = 30\\ \Leftrightarrow \frac{1}{6}\left| {\left[ {\overrightarrow {BC} ,\overrightarrow {BD} } \right],\overrightarrow {BA} } \right| = 30\\ \Leftrightarrow \left| { - 12\left( {a + 3} \right) - 24.0 + 24.10} \right| = 180\\ \Leftrightarrow \left| {a - 17} \right| = 15\\ \Leftrightarrow \left[ \begin{array}{l} a = 2\\ a = 32 \end{array} \right. \end{array}\)