Let the line \( L_1 \) be parallel to the vector \( -3\hat{\text{i}} + 2\hat{\text{j}} + 4\hat{\text{k}} \) and pass through the point \( (2,\, 6,\, 7) \), and the line \( L_2 \) be parallel to the vector \( 2\hat{\text{i}} + \hat{\text{j}} + 3\hat{\text{k}} \) and pass through the point \( (4,\, 3,\, 5) \). If the line \( L_3 \) is parallel to the vector \( -3\hat{\text{i}} + 5\hat{\text{j}} + 16\hat{\text{k}} \) and intersects the lines \( L_1 \) and \( L_2 \) at the points \( C \) and \( D \), respectively, then \( |\overline{CD}|^2 \) is equal to:
