# Find the equation of the plane through the points

Question:

Find the equation of the plane through the points $A(2,1,-1)$ and $B(-1,3,4)$ and perpendicular to the plane $x-2 y+4 z=10 .$ Also, show that

the plane thus obtained contains the line $\overrightarrow{\mathrm{r}}=(-\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}-5 \hat{\mathrm{k}})$

Solution: