Equation Of Line
Easymathematics
The symmetric form of equation of a line passing through (x₁, y₁, z₁) with direction ratios a, b, c is
Select the correct option:
Solution
Incorrect! 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.
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
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.
Looking for more practice? Explore all mathematics questions or browse three dimensional geometry questions on RankGuru.