On the coordinate plane, it is known that the orthogonal projection length of vector $\vec{v}$ in the direction of vector $(2, -3)$ is 1 less than its original length, and the orthogonal projection length in the direction of vector $(3, 2)$ is 2 less than its original length. If $\vec{v}$ makes acute angles with both vectors $(2, -3)$ and $(3, 2)$, then the orthogonal projection length of $\vec{v}$ in the direction of vector $(4, 7)$ is