Let a, b and c be three unit vectors such that a + b + c = 0. If λ= a · b + b · c + c · a and d = a × b + b × c + c × a, then the ordered pair, (λ, d…

Let $\displaystyle \vec{a}, \vec{b}$ and $\displaystyle \vec{c}$ be three unit vectors such that $\displaystyle \vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$.If $$\begin{aligned} & \lambda=\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a} \text { and } \\ & \vec{d}=\vec{a} \times \vec{b}+\vec{b} \times \vec{c}+\vec{c} \times \vec{a}, \text { then } \end{aligned} $$ the ordered pair, $\displaystyle (\lambda, \overrightarrow{\mathrm{d}})$ is equal to :