Cho \(K\left( {1\,;\,\,2\,;\,\,3} \right)\) và phương trình mặt phẳng \(\left( P \right):{\mkern 1mu} {\mkern 1mu} 2x - y + 3 = 0\).

Ta có \(\left\{ {\begin{array}{*{20}{l}}{\left( Q \right) \bot \left( P \right)}\\{\left( Q \right) \supset OK}\end{array}} \right. \Rightarrow \left\{ {\begin{array}{*{20}{l}}{{{\vec n}_{\left( Q \right)}} \bot {{\vec n}_{\left( P \right)}}}\\{{{\vec n}_{\left( Q \right)}} \bot \overrightarrow {OK} }\end{array}} \right. \Rightarrow {\vec n_{\left( Q \right)}} = \left[ {\overrightarrow {OK} \,;\,\,{{\vec n}_{\left( P \right)}}} \right]\)

Ta có \[\overrightarrow {OK} = \left( {1\,;\,\,2\,;\,\,3} \right)\,;\,\,{\mkern 1mu} {\vec n_{\left( P \right)}} = \left( {2\,;\,\, - 1\,;\,\,0} \right) \Rightarrow {\vec n_{\left( Q \right)}} = \left[ {\overrightarrow {OK} \,;\,\,{{\vec n}_{\left( P \right)}}} \right] = \left( {3\,;\,\,6\,;\,\, - 5} \right)\].

Vậy phương trình mặt phẳng \(\left( Q \right)\) là: \(3x + 6y - 5z = 0\).Chọn A.