Equation Of Line
The symmetric form of equation of a line passing through (x₁, y₁, z₁) with direction ratios a, b, c is
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About This Question
- Subject
- mathematics
- Chapter
- three dimensional geometry
- Topic
- equation of line
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
(x-x₁)/a = (y-y₁)/b = (z-z₁)/c
- Vector Theory: A line passing through point A=(x1,y1,z1) and parallel to a direction vector D=ai^+bj^+ck^ is given by r=A+λD.
- Cartesian Translation: Separating the components:
- x=x1+λa⟹λ=ax−x1
- y=y1+λb⟹λ=by−y1
- z=z1+λc⟹λ=cz−z1
- Symmetric Form: Equating the λ values: ax−x1=by−y1=cz−z1.
This easy difficulty mathematics question is from the chapter three dimensional geometry, covering the topic of equation of line. It appeared in the 2025 exam.
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