Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Here given plane passes through the point $(2,0,1)$ and let $\overline{\mathrm{b}}=\hat{\mathrm{i}}$ and $\bar{c}=\hat{i}+2\hat{j}-3\hat{k}$. Normal vector $\overline{\mathrm{n}}=\overline{\mathrm{b}}\times \overline{\mathrm{c}}=\left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ 1& 0& 0\\ 1& 2& -3\end{array}\right|=3\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ The equation of plane in scalar product from is $\overline{\mathrm{r}}\cdot \overline{\mathrm{n}}=\overline{\mathrm{a}}\cdot \overline{\mathrm{n}}$ Here $\bar{a}\cdot \bar{n}=(2\hat{i}+\hat{k})\cdot (3\hat{j}+2\hat{k})=2$ $\therefore \alpha =2$