List of top Mathematics Questions on 3D Geometry asked in JEE Advanced

Let \(P\) be the plane such that it contains the straight line \[ \frac{x-1}{2}=\frac{y-3}{3}=\frac{z+2}{1} \] and is perpendicular to the plane \[ x+2y+3z=4 \] Let \(P_1\) be the plane which passes through the point \((4,2,2)\) and is parallel to \(P\). Then which of the following statements is (are) TRUE?

Let $ L_1 $ be the line of intersection of the planes given by the equations $$ 2x + 3y + z = 4 \quad \text{and} \quad x + 2y + z = 5. $$ Let $ L_2 $ be the line passing through the point $ P(2, -1, 3) $ and parallel to $ L_1 $. Let $ M $ denote the plane given by the equation $$ 2x + y - 2z = 6. $$ Suppose that the line $ L_2 $ meets the plane $ M $ at the point $ Q $. Let $ R $ be the foot of the perpendicular drawn from $ P $ to the plane $ M $. Then which of the following statements is (are) TRUE?