If the three vectors \(\overrightarrow{p}=a\hat i+a\hat j+c\hat k\) \(\overrightarrow{q}=\hat i+\hat k \)  and \(\overrightarrow{r}=c\hat i+c\hat j+b\hat k \)  are coplanar.

I: c is the geometric mean of a and b.

II: \( (2\vec p × 3\vec q)⋅4\vec r + (5\vec q × 3\vec r)⋅6 \vec p\) equal to 1.

Which of the following statement(s) is/are correct?