Let \(\vec a = 2\hat i - 7\hat j + 5\hat k\), \(\vec b = \hat i + \hat k\) and \(\vec c = \hat i + 2\hat j - 3\hat k\) be three given vectors. If \(\vec r\) is a vector such that \(\vec r \times \vec a = \vec c \times \vec a\) and \(\vec r \cdot \vec b = 0\), then \(|\vec r|\) is equal to: