Let | a | $$\ne$$ 0, | b | $$\ne$$ 0. (a + b) . (a + b) = | a |² + | b |² holds if and only if

If $$r = x\widehat i + y\widehat j + z\widehat k$$, then what is $$r\,.\,\left( {\widehat i + \widehat j + \widehat k} \right)$$ equal to ?

A unit vector perpendicular to each of the vectors $$2\widehat i - \widehat j + \widehat k$$ and $$3\widehat i - 4\widehat j - \widehat k$$ is

If | a | = 3, | b | = 4 and | a $$-$$ b | = 5, then what is the value of | a + b | ?