Q88.If a plane passes through the points (−1, k, 0), (2, k, −1), (1, 1, 2) and is parallel to the line x−11 = 2y+12 = z+1−1 , then the value of (k−1)(k−2)k2+1 is (1) 17 (2) 5 5 17 (3) 6 (4) 13 13 6
What This Question Tests
This question tests the ability to determine the equation of a plane given three points and apply the condition for a plane to be parallel to a given line, thereby finding the unknown parameter 'k'.
Concepts Tested
Formulas Used
Equation of plane: A(x-x₁) + B(y-y₁) + C(z-z₁) = 0
Condition for plane and line parallelism: A L + B M + C N = 0
Vector normal to plane derived from three points: (P₂-P₁) x (P₃-P₁)
📚 NCERT Sections This Tests
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2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
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📋 Question Details
- Chapter
- 3D Geometry
- Topic
- Plane and Line in 3D
- Year
- 2023
- Shift
- 30 Jan Shift 2
- Q Number
- Q88
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 11: Three Dimensional Geometry
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