Let $$a=2i+j+k, b=i+2j-k$$ and a unit vector $$c$$ be coplanar. If $$c$$ is perpendicular to $$a,$$ then $$c =$$

Let $$a=2i+j-2k$$ and $$b=i+j.$$ If $$c$$ is a vector such that $$a.$$ $$c = \left| c \right|,\left| {c - a} \right| = 2\sqrt 2 $$ and the angle between $$\left( {a \times b} \right)$$ and $$c$$ is $${30^ \circ },$$ then $$\left| {\left( {a \times b} \right) \times c} \right| = $$

For three vectors $$u,v,w$$ which of the following expression is not equal to any of the remaining three?

If $$a = i + j + k,\overrightarrow b = 4i + 3j + 4k$$ and $$c = i + \alpha j + \beta k$$ are linearly dependent vectors and $$\left| c \right| = \sqrt 3 ,$$ then