Home/
Competitive Exams/
JEE Main & Advanced/
Mathematics/
Three Dimensional Geometry/
Question 350007
JEE Mathematics · Medium

Three Dimensional Geometry: Angle between lines MCQ

Solve this quality-checked JEE multiple-choice question, then review the correct answer and explanation.

Timer-based practiceDetailed answer reviewMobile-friendly flow
Angle between linesMediumQuestion 350007

Question

The angle θ between lines with direction ratios (a₁,b₁,c₁) and (a₂,b₂,c₂) satisfies:
  1. A
    cos θ = (a₁a₂+b₁b₂+c₁c₂)/(√(Σa₁²)√(Σa₂²))
    Correct
  2. B
    cos θ = a₁a₂+b₁b₂+c₁c₂
  3. C
    tan θ = a₁/a₂
  4. D
    sin θ = a₁b₂−a₂b₁

Correct answer

cos θ = (a₁a₂+b₁b₂+c₁c₂)/(√(Σa₁²)√(Σa₂²))

Explanation

cos θ = |a₁a₂+b₁b₂+c₁c₂| / (√(a₁²+b₁²+c₁²) × √(a₂²+b₂²+c₂²)). For perpendicular lines: a₁a₂+b₁b₂+c₁c₂ = 0.

Review Three Dimensional Geometry notesStart timed chapter practice