Q74.If the equation of a plane P , passing through the intersection of the planes, x + 4y −z + 7 = 0 and 3x + y + 5z = 8 is ax + by + 6z = 15 for some a, b ∈R, then the distance of the point (3, 2, −1) from the plane P is … …
What This Question Tests
This question involves finding the equation of a plane that passes through the intersection of two given planes and also satisfies a specific form, then calculating the perpendicular distance from a given point to this plane.
Concepts Tested
Formulas Used
P₁ + λP₂ = 0 for plane through intersection of P₁=0 and P₂=0
Distance of (x₁, y₁, z₁) from Ax+By+Cz+D=0 is |Ax₁+By₁+Cz₁+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.
2.5 — A Parallel Plate Capacitor With Air Between The Plates Has A
Physics Class 11 · Chapter 2
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?
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?
📋 Question Details
- Chapter
- 3D Geometry
- Topic
- Equation of a plane passing through intersection of two planes, Distance from a point to a plane
- Year
- 2020
- Shift
- 04 Sep Shift 1
- Q Number
- Q74
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 11: Three Dimensional Geometry
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