Выразите вектор MN через а и б.

$$\overrightarrow{AD} = \overrightarrow{a}$$ и $$\overrightarrow{CB} = \overrightarrow{b}$$.

$$\overrightarrow{MN} = \overrightarrow{MA} + \overrightarrow{AD} + \overrightarrow{DN}$$

$$\overrightarrow{MA} = -\overrightarrow{AM} = -\frac{1}{2} \overrightarrow{AC}$$

$$\overrightarrow{AC} = \overrightarrow{AD} + \overrightarrow{DC} = \overrightarrow{a} - \overrightarrow{b}$$

$$\overrightarrow{MA} = -\frac{1}{2} (\overrightarrow{a} - \overrightarrow{b}) = -\frac{1}{2} \overrightarrow{a} + \frac{1}{2} \overrightarrow{b}$$

$$\overrightarrow{DN} = \frac{1}{2} \overrightarrow{DB}$$

$$\overrightarrow{DB} = -\overrightarrow{AD} + \overrightarrow{AB} = -\overrightarrow{a} + \overrightarrow{b}$$

$$\overrightarrow{DN} = \frac{1}{2} (-\overrightarrow{a} + \overrightarrow{b}) = -\frac{1}{2} \overrightarrow{a} + \frac{1}{2} \overrightarrow{b}$$

$$\overrightarrow{MN} = -\frac{1}{2} \overrightarrow{a} + \frac{1}{2} \overrightarrow{b} + \overrightarrow{a} - \frac{1}{2} \overrightarrow{a} + \frac{1}{2} \overrightarrow{b} = (-\frac{1}{2} + 1 - \frac{1}{2}) \overrightarrow{a} + (\frac{1}{2} + \frac{1}{2}) \overrightarrow{b} = \overrightarrow{0a} + \overrightarrow{b}$$

$$\overrightarrow{MN} = \overrightarrow{b}$$