Find the vector equation of the line passing through the point with position vector
Question:

Find the vector equation of the line passing through the point with position vector $(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})$ and perpendicular to the plane $\overrightarrow{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}-\hat{\mathrm{k}})=0$

Solution: