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📐 Mathematics  ·  Three Dimensional Geometry  ·  JEE

The ratio in which plane x+y+z=9 divides segment from A(2,1,3) to B(5,4,6):

Answer: 1:2.

  • A 1:2
  • B 2:1
  • C 1:1
  • D 3:1

Correct answer: A. 1:2

Explanation: Point dividing AB in ratio k:1: ((5k+2)/(k+1),(4k+1)/(k+1),(6k+3)/(k+1)). Sum = (15k+6)/(k+1) = 9. So 15k+6 = 9k+9, 6k = 3, k = 1/2. Ratio = 1:2.

zxyOP (x, y, z)

Three mutually perpendicular axes x, y, z meeting at the origin O, with a point P located by its (x, y, z) coordinates.

Concept context

Lines and planes in 3D space, direction cosines, distances, and angles

Read the full Three Dimensional Geometry notes →