Zaymiey

📐 Mathematics  ·  Three Dimensional Geometry  ·  JEE

If a line makes angles alpha, beta, gamma with x, y, z axes respectively, then sin<sup>2</sup>(alpha)+sin<sup>2</sup>(beta)+sin<sup>2</sup>(gamma) =

Answer: 2.

  • A 1
  • B 3
  • C 0
  • D 2

Correct answer: D. 2

Explanation: l<sup>2</sup>+m<sup>2</sup>+n<sup>2</sup> = 1, where l=cos(alpha) etc. sin<sup>2</sup>(alpha)+sin<sup>2</sup>(beta)+sin<sup>2</sup>(gamma) = (1-cos<sup>2</sup>(alpha))+(1-cos<sup>2</sup>(beta))+(1-cos<sup>2</sup>(gamma)) = 3 - (l<sup>2</sup>+m<sup>2</sup>+n<sup>2</sup>) = 3 - 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 →