Let a, b and c be three non-zero non-coplanar vectors. Let the position vectors of four points A, B, C and D be a - b + c, λ a -3 b +4 c,- a +2 b -3…

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