Light ray incident along a vector \( \overrightarrow{AO} \, ( \overrightarrow{AO} = 2\hat{i} - 3\hat{j} ) \) emerges out along vector \( \overrightarrow{OB} \, ( \overrightarrow{OB} = C\hat{i} - 4\hat{j} ) \) as shown in the figure below. The value of \( C \) is _______.
