Question:
Find the vector equation of the plane passing through the intersection of the planes $\overrightarrow{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})=3$ and $\overrightarrow{\mathrm{r}} \cdot(3 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})+11=0$, and passing through the point $(-2,1,3)$.
Solution:
