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📐 Mathematics  ·  Three Dimensional Geometry  ·  JEE

Find the direction cosines of a line with direction ratios (2, -1, 2).

Answer: (2/3, -1/3, 2/3).

  • A (2/3, -1/3, 2/3)
  • B (2, -1, 2)
  • C (1/3, -1/3, 1/3)
  • D (4/9, 1/9, 4/9)

Correct answer: A. (2/3, -1/3, 2/3)

Explanation: Magnitude = sqrt(4+1+4) = 3. l = 2/3, m = -1/3, n = 2/3. Verify: (2/3)<sup>2</sup>+(-1/3)<sup>2</sup>+(2/3)<sup>2</sup> = 4/9+1/9+4/9 = 1.

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 →