Phương pháp giải:

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

Lời giải chi tiết:

\(\overrightarrow {AB}  = \left( {1; - 1;2} \right),\overrightarrow {AC}  = \left( {0; - 2;4} \right)\)

\(\left[ {\overrightarrow {AB} ,\overrightarrow {AC} } \right] = \left( {0; - 4; - 2} \right)\)

\(D \in Oy \Rightarrow D\left( {0;y;0} \right)\)\( \Rightarrow \overrightarrow {AD}  = \left( { - 2;y - 1;1} \right)\)

\(\begin{array}{l}V = \frac{1}{6}\left| {\overrightarrow {AD} .\left[ {\overrightarrow {AB} ,\overrightarrow {AC} } \right]} \right| = 5\\ \Leftrightarrow \left| {\overrightarrow {AD} .\left[ {\overrightarrow {AB} ,\overrightarrow {AC} } \right]} \right| = 30\end{array}\)

Nếu \(\overrightarrow {AD} .\left[ {\overrightarrow {AB} ,\overrightarrow {AC} } \right] = 30\) thì

\(\begin{array}{l}\left( { - 2} \right).0 + \left( {y - 1} \right).\left( { - 4} \right) + 1.\left( { - 2} \right) = 30\\ \Leftrightarrow y =  - 7 =  > D\left( {0; - 7;0} \right)\end{array}\)

Nếu \(\overrightarrow {AD} .\left[ {\overrightarrow {AB} ,\overrightarrow {AC} } \right] =  - 30\) thì

\(\begin{array}{l}\left( { - 2} \right).0 + \left( {y - 1} \right).\left( { - 4} \right) + 1.\left( { - 2} \right) =  - 30\\ \Leftrightarrow y = 8 \Rightarrow D\left( {0;8;0} \right)\end{array}\)