If four distinct points with position vectors \(\vec{a}, \vec{b}, \vec{c}\) and \(\vec{d}\) are coplanar; then \([\vec{a…

\([\vec{d} \vec{c} \vec{a}]+[\vec{b} \vec{d} \vec{a}]+[\vec{c} \vec{d} \vec{b}]\)

\([\vec{d} \vec{b} \vec{a}]+[\vec{a} \vec{c} \vec{d}]+[\vec{d} \vec{b} \vec{c}]\)

\([\vec{d} \vec{d} \vec{b}]+[\vec{d} \vec{c} \vec{a}]+[\vec{d} \vec{b} \vec{c}]\)

\([\vec{b} \vec{c} \vec{d}]+[\vec{d} \vec{a} \vec{c}]+[\vec{d} \vec{b} \vec{a}]\)