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

Let $$\overrightarrow a = \widehat i + 2\widehat j + \lambda \widehat k,\overrightarrow b = 3\widehat i - 5\widehat j - \lambda \widehat k,\overrightarrow a \,.\,\overrightarrow c = 7,2\overrightarrow b \,.\,\overrightarrow c + 43 = 0,\overrightarrow a \times \overrightarrow c = \overrightarrow b \times \overrightarrow c $$. Then $$\left| {\overrightarrow a \,.\,\overrightarrow b } \right|$$ is equal to :

Let $$\vec{a}$$ and $$\vec{b}$$ be two vectors such that $$|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}, \vec{a} \cdot \vec{b}=3$$ and $$|\vec{a} \times \vec{b}|^{2}=75$$. Then $$|\vec{a}|^{2}$$ is equal to __________.

Let $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be three non-coplanar vectors such that $$\overrightarrow a $$ $$\times$$ $$\overrightarrow b $$ = 4$$\overrightarrow c $$, $$\overrightarrow b $$ $$\times$$ $$\overrightarrow c $$ = 9$$\overrightarrow a $$ and $$\overrightarrow c $$ $$\times$$ $$\overrightarrow a $$ = $$\alpha$$$$\overrightarrow b $$, $$\alpha$$ > 0. If $$\left| {\overrightarrow a } \right| + \left| {\overrightarrow b } \right| + \left| {\overrightarrow c } \right| = {1 \over {36}}$$, then $$\alpha$$ is equal to __________.