Let the equation of the plane passing through the line x - 2y - z - 5 = 0 = x + y + 3z - 5 and parallel to the line x + y + 2z - 7 = 0 = 2x + 3y + z - 2 be ax + by + cz = 65. Then the distance of the point (a, b, c) from the plane 2x + 2y - z + 16 = 0 is _ _ _ _ _ _.

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 25 Jan, Morning shift · Q19

JEE Main 202325 Jan, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let the equation of the plane passing through the line

x - 2y - z - 5 = 0 = x + y + 3z - 5

and parallel to the line

x + y + 2z - 7 = 0 = 2x + 3y + z - 2

ax + by + cz = 65

. Then the distance of the point (a, b, c) from the plane

2x + 2y - z + 16 = 0

is ____________.

Your answerType your answer. Integers and decimals are accepted.