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 position vectors of the points X and Y be i - 2 j + 4 k and 5 i - j + 2 k respectively. Then the points:

(C) X and Y are on the opposite sides of P

(A) X and X + Y are on the same side of P

(B) Y and Y - X are on the opposite sides of P

(D) X + Y and X - Y are on the same side of P

Three Dimensional Geometry: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Evening shift · Q2593

JEE Main 202225 Jun, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let p be the plane passing through the intersection of the planes

\overrightarrow r \,.\,\left( {\widehat i + 3\widehat j - \widehat k} \right) = 5

and

\overrightarrow r \,.\,\left( {2\widehat i - \widehat j + \widehat k} \right) = 3

, and the point (2, 1,

-

2). Let the position vectors of the points X and Y be

\widehat i - 2\widehat j + 4\widehat k

and

5\widehat i - \widehat j + 2\widehat k

respectively. Then the points :