Let three vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be such that $$\overrightarrow c $$ is coplanar
with $$\overrightarrow a $$ and $$\overrightarrow b $$, $$\overrightarrow a .\overrightarrow c $$ = 7 and $$\overrightarrow b $$ is perpendicular to $$\overrightarrow c $$, where
$$\overrightarrow a = - \widehat i + \widehat j + \widehat k$$ and $$\overrightarrow b = 2\widehat i + \widehat k$$ , then the
value of $$2{\left| {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right|^2}$$ is _____.

If $$\overrightarrow x $$ and $$\overrightarrow y $$ be two non-zero vectors such that $$\left| {\overrightarrow x + \overrightarrow y } \right| = \left| {\overrightarrow x } \right|$$ and $${2\overrightarrow x + \lambda \overrightarrow y }$$ is perpendicular to $${\overrightarrow y }$$, then the value of $$\lambda $$ is _________ .

If $$\overrightarrow a $$ and $$\overrightarrow b $$ are unit vectors, then the greatest value of

$$\sqrt 3 \left| {\overrightarrow a + \overrightarrow b } \right| + \left| {\overrightarrow a - \overrightarrow b } \right|$$ is_____.

Let the vectors $$\overrightarrow a $$, $$\overrightarrow b $$, $$\overrightarrow c $$ be such that
$$\left| {\overrightarrow a } \right| = 2$$, $$\left| {\overrightarrow b } \right| = 4$$ and $$\left| {\overrightarrow c } \right| = 4$$. If the projection of
$$\overrightarrow b $$ on $$\overrightarrow a $$ is equal to the projection of $$\overrightarrow c $$ on $$\overrightarrow a $$
and $$\overrightarrow b $$ is perpendicular to $$\overrightarrow c $$, then the value of
$$\left| {\overrightarrow a + \vec b - \overrightarrow c } \right|$$ is ___________.