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

• A

  $X$ and $X+Y$ are on the same side of $P$
• B

  $Y$ and $Y-X$ are on the opposite sides of $P$
• Correct answer
  C

  $X$ and $Y$ are on the opposite sides of $P$
• D

  $X+Y$ and $X-Y$ are on the same side of $P$

Hence, the correct answer is option: 'C'.