Đáp án:
\(M\left( {0;7} \right).\)
Giải thích các bước giải:
\(\eqalign{
& Goi\,\,M\left( {0;m} \right) \in Oy \cr
& Ta\,\,co:\,\,\overrightarrow {MP} = \left( {4;1 - m} \right);\,\,\overrightarrow {MQ} = \left( { - 1;3 - m} \right) \cr
& \,\,\,2\overrightarrow {MP} - 3\overrightarrow {MQ} \cr
& = 2\left( {4;1 - m} \right) - 3\left( { - 1;3 - m} \right) \cr
& = \left( {8;2 - 2m} \right) - \left( { - 3;9 - 3m} \right) \cr
& = \left( {11;m - 7} \right) \cr
& \Rightarrow \left| {2\overrightarrow {MP} - 3\overrightarrow {MQ} } \right| = \sqrt {{{11}^2} + {{\left( {m - 7} \right)}^2}} \ge 11 \cr
& \Rightarrow {\left| {2\overrightarrow {MP} - 3\overrightarrow {MQ} } \right|_{\min }} = 11 \Leftrightarrow m = 7 \cr
& Vay\,\,M\left( {0;7} \right). \cr} \)
