Q78.The length of the perpendicular from the point (1, −2, 5) on the line passing through (1, 2, 4) and parallel to the line x + y −z = 0 = x −2y + 3z −5 is: (1) √212 (2) √92 (3) √732 (4) 1
What This Question Tests
This question requires finding the direction vector of a line defined by the intersection of two planes and then calculating the perpendicular distance from a given point to this line in 3D space.
Concepts Tested
Formulas Used
Direction ratios of line of intersection of A₁x+B₁y+C₁z+D₁=0 and A₂x+B₂y+C₂z+D₂=0 are (B₁C₂-B₂C₁, C₁A₂-C₂A₁, A₁B₂-A₂B₁)
Vector method for distance of point from line: |(AP × b)| / |b|
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📋 Question Details
- Chapter
- 3D Geometry
- Topic
- Lines in 3D and Perpendicular Distance
- Year
- 2022
- Shift
- 26 Jul Shift 1
- Q Number
- Q78
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 11: Three Dimensional Geometry
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