Perpendicular Lines
Two lines with direction ratios (a₁, b₁, c₁) and (a₂, b₂, c₂) are perpendicular if
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About This Question
- Subject
- mathematics
- Chapter
- three dimensional geometry
- Topic
- perpendicular lines
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
a₁a₂ + b₁b₂ + c₁c₂ = 0
- Theory: Two lines are perpendicular if the angle θ between them is 90∘, which means cos90∘=0.
- Calculation: Using the direction ratio vectors v1=(a1,b1,c1) and v2=(a2,b2,c2).
- Condition: v1⋅v2=0⟺a1a2+b1b2+c1c2=0.
This easy difficulty mathematics question is from the chapter three dimensional geometry, covering the topic of perpendicular lines. It appeared in the 2025 exam.
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