Sign change under interchange in scalar triple product for JEE

Formula

\(\vec{a}\cdot(\vec{b}\times\vec{c})=-\vec{a}\cdot(\vec{c}\times\vec{b})\)

Variables: \(\vec{a},\vec{b},\vec{c}\) are vectors.

Conditions: Interchanging any two vectors changes the sign.

Handling orientation and determinant sign.