Equation Of Plane
Mediummathematics
The equation of plane passing through (1, 2, 3) and perpendicular to line with direction ratios 2, 3, 4 is
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Solution
Incorrect! Answer:
2x + 3y + 4z = 20
- Identify Normal: A plane perpendicular to a line has the line's direction ratios as its normal vector. Here, n=(2,3,4).
- Point-Normal Form: Use the formula A(x−x1)+B(y−y1)+C(z−z1)=0.
- Substitution: Substitute point (1,2,3) and normal coefficients: 2(x−1)+3(y−2)+4(z−3)=0
- Simplification: 2x−2+3y−6+4z−12=0⟹2x+3y+4z−20=0 ∴2x+3y+4z=20.
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About This Question
- Subject
- mathematics
- Chapter
- three dimensional geometry
- Topic
- equation of plane
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
2x + 3y + 4z = 20
- Identify Normal: A plane perpendicular to a line has the line's direction ratios as its normal vector. Here, n=(2,3,4).
- Point-Normal Form: Use the formula A(x−x1)+B(y−y1)+C(z−z1)=0.
- Substitution: Substitute point (1,2,3) and normal coefficients: 2(x−1)+3(y−2)+4(z−3)=0
- Simplification: 2x−2+3y−6+4z−12=0⟹2x+3y+4z−20=0 ∴2x+3y+4z=20.
This medium difficulty mathematics question is from the chapter three dimensional geometry, covering the topic of equation of plane. It appeared in the 2025 exam.
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