Mathematics Question from JEE Main 2023 · 29 January, Shift 1

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