Let P be the plane passing through the intersection of the planes r ·( i +3 j - k )=5 and r ·(2 i - j + k )=3, and the point (2,1,-2). Let the…

Let $\displaystyle P$ be the plane passing through the intersection of the planes $\displaystyle \vec{r} \cdot(\hat{i}+3 \hat{j}-\hat{k})=5$ and $\displaystyle \vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=3$, and the point $\displaystyle (2,1,-2)$. Let the position vectors of the points $\displaystyle X$ and $\displaystyle Y$ be $\displaystyle \hat{i}-2 \hat{j}+4 \hat{k}$ and $\displaystyle 5 \hat{i}-\hat{j}+2 \hat{k}$ respectively. Then the points