Let \( \vec{a}, \ \vec{b} \) and \( \vec{c} \) be three non-zero non-coplanar vectors. Let the position vectors of four points \( A, B, C \) and \( D \) be \( \vec{a} - \vec{b} + \vec{c} \), \( \lambda \vec{a} - 3\vec{b} + 4\vec{c} \), \( -\vec{a} + 2\vec{b} - 3\vec{c} \) and \( 2\vec{a} - 4\vec{b} + 6\vec{c} \) respectively. If \( \overrightarrow{AB}, \ \overrightarrow{AC} \) and \( \overrightarrow{AD} \) are coplanar, then \( \lambda \) is equal to __________ .
