Home › UP Board Class 12 › Mathematics › Three Dimensional Geometry › The angle between the lines with direction ratio…
The angle between the lines with direction ratios (1, 2, 2) and (2, 1, 2) satisfies
Acos⁻¹(4/9)
Bcos⁻¹(8/9)
Ccos⁻¹(6/9)
D90°
Answer & Solution
Correct answer: B. cos⁻¹(8/9)
1. Dot product: 1·2 + 2·1 + 2·2 = 2 + 2 + 4 = 8.
2. Magnitudes: √(1+4+4) = 3 for each direction vector.
3. cos θ = 8 / (3·3) = 8/9.
4. So θ = cos⁻¹(8/9).
_Source: NCERT Class 12 Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.4_
Related questions
The image of the point (1, 2, 3) in the plane x + y + z = 0 isThe foot of the perpendicular from origin to the plane 2x + 3y - 6z = 14 isThe line through the origin with direction ratios (1, 1, 1) meets the plane x + y + z = 6 A line has direction ratios (1, 1, 2) and meets the plane x - y + z = 0. The angle ϕ betweThe plane through the points (1,1,0), (1,0,1) and (0,1,1) has equationThe equation of a plane parallel to x + 2y - 3z = 5 and passing through (1, 1, 1) isThe shortest distance between r = (1,2,3) + λ(2,3,4) and r = (2,4,5) + μ(3,4,5) isThe line r = (2, -1, 4) + λ(3, 0, 2), expressed in symmetric Cartesian form, is