Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\).…

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

[JEE Main 2020, 7 Jan (Shift 2)]