Let P be the plane passing through the points (5,3,0),(13,3,-2) and (1,6,2). For α N, if the distances of the points A(3,4, α) and B(2, α, a) from the plane P are 2 and 3 respectively, then the positive value of a is:

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Evening shift · Q2610

JEE Main 202311 Apr, Evening shiftMathematicsHardThree Dimensional Geometry249× since 2002

Let P be the plane passing through the points

(5,3,0),(13,3,-2)

and

(1,6,2)

. For

\alpha \in \mathbb{N}

, if the distances of the points

\mathrm{A}(3,4, \alpha)

and

\mathrm{B}(2, \alpha, a)

from the plane P are 2 and 3 respectively, then the positive value of a is :