Câu hỏi 31

Ta có: hai vecto \(\overrightarrow a  = \left( {m;\,\,2;\,\,3} \right)\) và \(\overrightarrow b  = \left( {1;\,\,n;\,\,2} \right)\) cùng phương \( \Leftrightarrow \overrightarrow a  = k\overrightarrow b \,\,\left( {k \ne 0} \right)\)

\(\begin{array}{l} \Leftrightarrow \left( {m;\,\,2;\,\,3} \right) = k\left( {1;\,\,n;\,\,2} \right) \Leftrightarrow \left\{ \begin{array}{l}m = k\\2 = kn\\3 = 2k\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}k = \dfrac{3}{2}\\m = \dfrac{3}{2}\\n = \dfrac{4}{3}\end{array} \right.\\ \Rightarrow 2m + 3n = 2.\dfrac{3}{2} + 3.\dfrac{4}{3} = 7.\end{array}\)

Chọn  D.