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:
