If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three mutually perpendicular unit vectors and \(...

If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three mutually perpendicular unit vectors and \( \vec{d} \) is a unit vector which makes equal angle with \( \vec{a}, \vec{b} \) and \( \vec{c} \) then \( |\vec{a}+\vec{b}+\vec{c}+\vec{d}|^{2} \) is equal to
(a) 4
(b) \( 4 \pm \sqrt{3} \)
(c) \( 4 \pm 2 \sqrt{3} \)
(d) \( 2 \pm 4 \sqrt{3} \)