If $\vec a,\vec b$ and $\vec c$ are unit coplanar vectors, then the scalar triple product $\begin{vmatrix}2\vec a-\vec b&2\vec b-\vec c&2\vec c-\vec a\end{vmatrix}=$
Answer & explanation
Correct answer: option 1
Since $\vec a,\vec b,\vec c$ are coplanar vectors.
$∴[\vec a\,\,\vec b\,\,\vec c]=0$
Let $\vec α =2\vec a-\vec b, \vec β =2\vec b-\vec c$, and $\vec γ = 2\vec c - \vec a$. Then,
$[\vec α\,\,\vec β\,\,\vec γ]=\begin{vmatrix}2&-1&0\\0&2&-1\\-1&0&2\end{vmatrix}[\vec a\,\,\vec b\,\,\vec c]$
$⇒[\vec α\,\,\vec β\,\,\vec γ]=7[\vec a\,\,\vec b\,\,\vec c]=7×0=0$