If a $$\times$$ b = c and b $$\times$$ c = a, then which one of the following is correct

If $$a = 2\widehat i + 3\widehat j + 4\widehat k$$ and $$b = 3\widehat i + 2\widehat j - \lambda \widehat k$$ are perpendicular, then what is the value of $$\lambda$$ ?

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 ?