Q89.Let the equation of the plane passing through the line x −2y −z −5 = 0 = x + y + 3z −5 and parallel to the line x + y + 2z −7 = 0 = 2x + 3y + z −2 be ax + by + cz = 65. Then the distance of the point (a, b, c) from the plane 2x + 2y −z + 16 = 0 is _____ .
What This Question Tests
This complex question involves finding a plane passing through the intersection of two planes and parallel to a given line, then calculating the distance of a point from another plane.
Concepts Tested
Formulas Used
Plane through intersection: P1 + λP2 = 0
Condition for parallel line and plane: a⋅d = 0 (normal vector ⋅ direction vector = 0)
Distance of (x0, y0, z0) from ax+by+cz+d=0 is |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.
2.5 — 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
- Year
- 2023
- Shift
- 25 Jan Shift 1
- Q Number
- Q89
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 11: Three Dimensional Geometry
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