Gọi \(M({x_M};{y_M})\)

Vì M ∈ Oy ⇒ M(0;\({y_M}\))

Ta có:

\(\overrightarrow {MA} = (2 - 0;3 - {y_M}) = (2;3 - {y_M})\)

\(\overrightarrow {MB} = \left( {4 - 0; - 1 - {y_M}} \right) = \left( {4; - 1 - {y_M}} \right) \Rightarrow k\overrightarrow {MB} = \left( {4k; - 1k - {y_M}k} \right)\)

Khi đó: \(\overrightarrow {MA} = k\overrightarrow {MB} \)

\( \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{2 = 4k}\\{3 - {y_M} = - 1k - {y_M}k}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{k = \frac{1}{2}}\\{3 - {y_M} = - 1k - {y_M}k}\end{array}} \right.\)

\( \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{k = \frac{1}{2}}\\{3 - {y_M} = - 1.\frac{1}{2} - {y_M}.\frac{1}{2}}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{k = \frac{1}{2}}\\{3 - {y_M} = - \frac{1}{2} - \frac{1}{2}{y_M}}\end{array}} \right.\)

\( \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{k = \frac{1}{2}}\\{ - {y_M} + \frac{1}{2}{y_M} = - \frac{1}{2} - 3}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{k = \frac{1}{2}}\\{ - \frac{1}{2}{y_M} = - \frac{7}{2}}\end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}}{k = \frac{1}{2}}\\{{y_M} = 7}\end{array}} \right.\)

Vậy giá trị của k là \(\frac{1}{2}\).