Answer: (1/sqrt(3),1/sqrt(3),1/sqrt(3)).
- A (1,1,1), an unnormalized direction vector
- B (1/sqrt(2),1/sqrt(2),0), normalized in only two axes
- C (1/3,1/3,1/3), a vector that is not properly normalized
- D (1/sqrt(3),1/sqrt(3),1/sqrt(3))
Correct answer: D. (1/sqrt(3),1/sqrt(3),1/sqrt(3))
Explanation: If l = m = n, then l²+m²+n² = 1 → 3l² = 1 → l = 1/√3. Direction cosines: (1/√3, 1/√3, 1/√3). Each makes angle cos⁻¹(1/√3) ≈ 54.7° with each axis. Answer: (1/√3, 1/√3, 1/√3).
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