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📐 Mathematics  ·  Three Dimensional Geometry  ·  JEE

The plane through line of intersection of x+y+z=1 and 2x+3y+4z=5 and parallel to x-axis has equation:

Answer: y + 2z = 3.

  • A y + 2z = 3
  • B x - y + z = 0
  • C y - z = 1
  • D x + y = 2

Correct answer: A. y + 2z = 3

Explanation: Family: (x+y+z-1)+k(2x+3y+4z-5)=0. Coefficient of x = 1+2k = 0, so k = -1/2. Plane: 0*x + (1-3/2)y + (1-2)z = 1-5/2, giving (-1/2)y + (-1)z = -3/2, so y + 2z = 3.

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

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