Home › Maharashtra HSC Class 12 (Science) › mathematics › Line and Plane › If l, m, n are direction cosines of a line then
If l, m, n are direction cosines of a line then
Al² + m² + n² = 1
Bl + m + n = 1
Cl m n = 0
Dl² + m² + n² = 0
Answer & Solution
Correct answer: A. l² + m² + n² = 1
1. Direction cosines are cosines of angles that the line makes with positive x-, y-, z-axes.
2. By the Pythagorean theorem in 3D, cos²α + cos²β + cos²γ = 1.
3. Hence l² + m² + n² = 1.
_Source: Maharashtra Balbharati Std XII Mathematics Part 1, Ch 6 "Line and Plane" §6.2_
Related questions
The plane x + y + z = 3 cuts intercepts on the coordinate axes equal toAngle between line with direction ratios (2, 1, 2) and plane 3x − 2y + 6z + 1 = 0Shortest distance between two skew lines is the length of the commonEquation of x-axis in 3D isTwo planes a₁x + b₁y + c₁z = d₁ and a₂x + b₂y + c₂z = d₂ are perpendicular iffPerpendicular distance from the point (1, 2, 3) to the plane 2x + 3y + 6z − 7 = 0 isEquation of a plane passing through point with position vector a and having normal n isTwo lines r = a₁ + s b₁ and r = a₂ + t b₂ are parallel iff