Cho \(A\left( {2;1; - 1} \r...

B

- Hướng dẫn giải

\(\begin{array}{l}D \in Oy \Rightarrow D\left( {0;y;0} \right)\\A\left( {2;1; - 1} \right),B\left( {3;0;1} \right),C\left( {2; - 1;3} \right)\\\overrightarrow {AB} = \left( {1; - 1;2} \right);\overrightarrow {AC} = \left( {0; - 2;4} \right)\\\overrightarrow {AD} = \left( { - 2;y - 1;1} \right)\\V = \frac{1}{6}\left| {\overrightarrow {AD} .\left[ {\overrightarrow {AB} ;\overrightarrow {AC} } \right]} \right|\\ = \frac{1}{6}\left| {\left( { - 2;y - 1;1} \right).\left( {0; - 4; - 2} \right)} \right|\\ = \frac{1}{6}\left| { - 4\left( {y - 1} \right) + 1\left( { - 2} \right)} \right| = \frac{1}{3}\left| {2y - 1} \right|\\V = 5 \Leftrightarrow y = - 7;y = 8\end{array}\)