Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Note that $(-1,1,2)$ is satisfied by only option (B) Alternate Method: Let $A\equiv (-1,1,2)$ $$\begin{array}{rl}\therefore \bar{a}& =-\hat{i}+\hat{j}+2\hat{k}\\ & \bar{n}=\hat{i}+\hat{j}+\hat{k}\end{array}$$ $\therefore$ equation of plane is $\overline{\mathrm{r}}\cdot \overline{\mathrm{n}}=\overline{\mathrm{a}}\cdot \overline{\mathrm{n}}$ $$\begin{array}{rl}& \Rightarrow \overline{\mathrm{r}}\cdot (\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})=(-\hat{\mathrm{i}}+\hat{\mathrm{j}}+2\hat{\mathrm{k}})\cdot (\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})\\ & \Rightarrow \overline{\mathrm{r}}\cdot (\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})=2\\ & \Rightarrow (x\hat{\mathrm{i}}+y\hat{\mathrm{j}}+\mathrm{z}\hat{\mathrm{k}})\cdot (\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})=2\\ & \Rightarrow x+y+\mathrm{z}-2=0\end{array}$$