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📐 Mathematics  ·  Three Dimensional Geometry  ·  JEE

The line through A(1,2,3) and B(4,5,6) meets the plane x+y+z=9 at:

Answer: (2,3,4).

  • A A itself
  • B (2,3,4)
  • C (3,4,2)
  • D B itself

Correct answer: B. (2,3,4)

Explanation: Direction AB=(3,3,3) or (1,1,1). Parametric: (1+t,2+t,3+t). On plane: (1+t)+(2+t)+(3+t) = 9, so 6+3t = 9, t = 1. Point = (2,3,4).

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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