Let $$a$$ and $$b$$ two non-collinear unit vectors. If $$u = a - \left( {a\,.\,b} \right)\,b$$ and $$v = a \times b,$$ then $$\left| v \right|$$ is

Which of the following expressions are meaningful?

The vector $$\,{1 \over 3}\left( {2\widehat i - 2\widehat j + \widehat k} \right)$$ is

Let $$\vec a = 2\hat i - \hat j + \hat k,\vec b = \hat i + 2\hat j - \hat k$$ and $$\overrightarrow c = \widehat i + \widehat j - 2\widehat k - 2\widehat k$$ be three vectors. A vector in the plane of $${\overrightarrow b }$$ and $${\overrightarrow c }$$, whose projection on $${\overrightarrow a }$$ is of magnitude $$\sqrt {2/3,} $$ is :