Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Here $\bar{a}=\hat{i}-\hat{j}+\hat{k}$ $\&\bar{n}=2\hat{i}+3\hat{j}-4\hat{k}$ Now $\bar{a}\cdot \bar{n}=2-3-4=-5$ Vector equation of plane passing through $\mathrm{A}(\bar{a})$ is $$\begin{array}{rl}& \overline{\mathrm{r}}\cdot \overline{\mathrm{n}}=\overline{\mathrm{a}}\cdot \overline{\mathrm{n}}\\ \Rightarrow & \overline{\mathrm{r}}\cdot (2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-4\hat{\mathrm{k}})=-5\end{array}$$