📐 Mathematics · Three Dimensional Geometry · JEE

If a line makes angles alpha, beta, gamma with x, y, z axes respectively, then sin²(alpha)+sin²(beta)+sin²(gamma) =

Answer: 2.

Correct answer: D. 2

Explanation: l²+m²+n² = 1, where l=cos(alpha) etc. sin²(alpha)+sin²(beta)+sin²(gamma) = (1-cos²(alpha))+(1-cos²(beta))+(1-cos²(gamma)) = 3 - (l²+m²+n²) = 3 - 1 = 2.

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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If a line makes angles alpha, beta, gamma with x, y, z axes respectively, then sin2(alpha)+sin2(beta)+sin2(gamma) =

Concept context

More Three Dimensional Geometry questions

If a line makes angles alpha, beta, gamma with x, y, z axes respectively, then sin²(alpha)+sin²(beta)+sin²(gamma) =