Let the vectors \( \vec{a}, \vec{b}, \vec{c} \) be such that \( |\vec{a}|=2,|\vec{b}|=4 \) and \( |\vec{c}|=4 \). If the…

Let the vectors \( \vec{a}, \vec{b}, \vec{c} \) be such that \( |\vec{a}|=2,|\vec{b}|=4 \) and \( |\vec{c}|=4 \). If the projection of \( \vec{b} \) on \( \vec{a} \) is equal to the projection of \( \vec{c} \) on \( \vec{a} \) and \( \vec{b} \) is perpendicular to \( \vec{c} \), then the value of \( |\vec{a}+\vec{b}-\vec{c}| \) is_________.

[JEE Main 2020, 5 Sep (Shift 2)]