Q89.Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, โ3, 1) and (2, 3, โ5) at the right angles. If a, b, c, d are integers, then the minimum value of (a2 + b2 + c2 + d2) is
What This Question Tests
This problem involves finding the midpoint of a line segment and determining the direction ratios of the line. These are then used as the normal vector and a point on the plane to establish its equation, ultimately leading to finding integer coefficients and minimizing the sum of their squares.
Concepts Tested
Formulas Used
Midpoint: ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2)
Equation of plane: a(x-x0) + b(y-y0) + c(z-z0) = 0
Direction Ratios: (x2-x1, y2-y1, z2-z1)
๐ NCERT Sections This Tests
2.1 โ Two Charges 5 ร 10โ8 C And โ3 ร 10โ8 C Are Located 16 Cm Apart. At
Physics Class 11 ยท Chapter 2
2.1 Two charges 5 ร 10โ8 C and โ3 ร 10โ8 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 โ Two Charges 2 Mc And โ2 Mc Are Placed At Points A And B 6 Cm
Physics Class 11 ยท Chapter 2
2.3 Two charges 2 mC and โ2 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 โ A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 ยท 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.
๐ Question Details
- Chapter
- 3D Geometry
- Topic
- Plane bisecting a line segment perpendicularly
- Year
- 2021
- Shift
- 18 Mar Shift 1
- Q Number
- Q89
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 11: Three Dimensional Geometry
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