Let \( P \) be the plane passing through the intersection of the planes \( \boldsymbol{r} \cdot(\hat{\boldsymbol{i}}+3 \hat{\boldsymbol{j}}-\hat{\boldsymbol{k}})=5 \) and \( \boldsymbol{r} \cdot(\widehat{2 \boldsymbol{i}}-3 \hat{\boldsymbol{j}}+\hat{\boldsymbol{k}})=3 \) and the point \( (2,1,-2) \). Let the position vectors of the points \( X \) and \( Y \) be \( \hat{\boldsymbol{i}}-2 \hat{\boldsymbol{j}}+4 \hat{\boldsymbol{k}} \) and \( 5 \hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+2 \hat{\boldsymbol{k}} \) repectively. 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 \( P \)
(c) \( X \) are \( Y \) on the opposite sides of \( P \)
(d) \( X+Y \) and \( X-Y \) are on the same side of \( P \)
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