Zaymiey

📐 Mathematics  ·  Three Dimensional Geometry  ·  JEE

The ratio in which the plane x+y+z=6 divides the segment joining (1,1,1) and (4,4,4):

Answer: 1:2.

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

Correct answer: B. 1:2

Explanation: Point dividing in ratio k:1: ((4k+1)/(k+1),(4k+1)/(k+1),(4k+1)/(k+1)). Sum = 3(4k+1)/(k+1) = 6. So 12k+3 = 6k+6, 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 →