alleryFor direction cosines l, m, n of any line in 3D:
AThe simple sum equals one: $l + m + n = 1$
BPythagorean $l^2 + m^2 + n^2 = 1$
CThe simple sum equals zero: $l + m + n = 0$
DThe product equals one: $l × m × n = 1$
Answer & Solution
Correct answer: B. Pythagorean $l^2 + m^2 + n^2 = 1$
**Always:** l² + m² + n² = 1, where l, m, n are cosines of angles with x, y, z axes.
This is the Pythagorean condition for a unit vector.
Keep practising Vector Algebra and 3D Geometry
Browse all Vector Algebra and 3D Geometry questions for GRE, or explore more Mathematics topics.
Related questions
A UNIT VECTOR in the direction of v = 3i + 4j is:The scalar triple product [a b c] geometrically represents:The Cartesian equation of a plane with intercepts 2, 3, 6 on the x, y, z axes is:The vector triple product a × (b × c) simplifies via:The angle θ between two PLANES with normals n1 and n2 satisfies:If a = 2i + 3j + k and b = i − j + 2k, then a · b equals:Two non-zero vectors a and b are PERPENDICULAR if and only if:Three vectors $\vec a, \vec b, \vec c$ are coplanar if and only if: