Q87.Let P be the plane passing through the points (5, 3, 0), (13, 3, −2) and (1, 6, 2). For α ∈N, if the distance of the points A(3, 4, α) and B(2, α, a) from the plane P are 2 and 3 respectively, then the positive value of a is (1) 6 (2) 3 (3) 5 (4) 4
What This Question Tests
This question involves finding the equation of a plane from three given points, then using the formula for the distance of a point from a plane for two different points to solve for the unknown parameter 'a'.
Concepts Tested
Formulas Used
Equation of plane: ax + by + cz = d (or Normal form)
Distance from point (x₀,y₀,z₀) to plane Ax+By+Cz+D=0: |Ax₀+By₀+Cz₀+D|/√(A²+B²+C²)
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
2.3 — Two Charges 2 Mc And –2 Mc Are Placed At Points A And B 6 Cm
Physics Class 11 · Chapter 2
2.3 Two charges 2 mC and –2 mC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system. (b) What is the direction of the electric field at every point on this surface?
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
📋 Question Details
- Chapter
- 3D Geometry
- Topic
- Equation of a plane, Distance of a point from a plane
- Year
- 2023
- Shift
- 11 Apr Shift 2
- Q Number
- Q87
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 11: Three Dimensional Geometry
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