Find the vector equation of the plane passing through the points $\left(2,1,1\right)and\left(1,3,4\right)$and perpendicular to the plane $x-2y+4z=10$. Also show that the plane thus obtained contains the line $\vec{r}=-\hat{i}+3\hat{j}+4\hat{k}+\lambda \left(3\hat{i}-2\hat{j}-5\hat{k}\right)\dot{}$

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