Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

We have $\bar{a}=3\hat{i}+\hat{j}-\hat{k},\bar{b}=2\hat{i}-\hat{j}+23\hat{k}$ and $\bar{c}=7\hat{i}-\hat{j}+23\hat{k}$ $\bar{a}\cdot \bar{b}=6-1-23\ne 0$ and $\bar{b}\cdot \bar{c}=14+1+529\ne 0$ Thus $\bar{a},\bar{b},\bar{c}$ are non mutually perpendicular. Also for $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}},\frac{3}{2}\ne -1\ne \frac{-1}{23}$. Thus $\bar{a}$ and $\bar{b}$ are not collinear. Now $\left|\begin{array}{ccc}3& 1& -1\\ 2& -1& 23\\ 7& -1& 23\end{array}\right|=3(-23+23)-(46-161)-(-2+7)\ne 0$. Thus $\bar{a},\bar{b},\bar{c}$ are non coplanar.