If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit coplanar vectors, then the scalar triple product $\left

Question

If $\vec{a}, \vec{b}$ and $\vec{c}$ are unit coplanar vectors, then the scalar triple product $\left[\begin{array}{llll}2 \vec{a}-\vec{b} & 2 \vec{b}-\vec{c} & 2 \vec{c}-\vec{a}\end{array}ight]=$\

Professor PC Thomas Classes · Answer

(a) : Since $\vec{a}, \vec{b}, \vec{c}$ are coplanar vectors,\ $2 \vec{a}-\vec{b}, 2 \vec{b}-\vec{c}, 2 \vec{c}-\vec{a}$ are also coplanar vectors.\ $	herefore \quad[2 \vec{a}-\vec{b}, 2 \vec{b}-\vec{c}, 2 \vec{c}-\vec{a}]=0$\