Find the point in yz-plane which is equidistant from the points A(3, 2, -1), B(1, -1, 0) and C(2, 1, 2).
The general point on yz plane is D(0, y, z). Consider this point is equidistant to the points A(3, 2, -1), B(1, -1, 0) and C(2, 1, 2).
$\therefore \mathrm{AD}=\mathrm{BD}$
$\sqrt{(0-3)^{2}+(y-2)^{2}+(z+1)^{2}}=\sqrt{(0-1)^{2}+(y+1)^{2}+(z-0)^{2}}$
Squaring both sides,
$(0-3)^{2}+(y-2)^{2}+(z+1)^{2}=(0-1)^{2}+(y+1)^{2}+(z-0)^{2}$
$9+y^{2}-4 y+4+z^{2}+2 z+1=1+y^{2}+2 y+1+z^{2}$
$-6 y+2 z+12=0$ ….(1)
Also, AD = CD
$\sqrt{(0-3)^{2}+(y-2)^{2}+(z+1)^{2}}=\sqrt{(0-2)^{2}+(y-1)^{2}+(z-2)^{2}}$
Squaring both sides,
$(0-3)^{2}+(y-2)^{2}+(z+1)^{2}=(0-2)^{2}+(y-1)^{2}+(z-2)^{2}$
$9+y^{2}-4 y+4+z^{2}+2 z+1=4+y^{2}-2 y+1+z^{2}-4 z+4$
$-2 y+6 z+5=0$ ..........(2)
Simultaneously solving equation (1) and (2) we get
$Y=31 / 16, z=-3 / 16$
The point which is equidistant to the points A(3, 2, -1), B(1, -1, 0) and C(2, 1, 2) is (0, 31/16, -3/16).
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,