Question:
The sum of the distinct real values of $\mu$, for which the vectors, $\mu \hat{i}+\hat{j}+\hat{k}, \quad \hat{i}+\mu \hat{j}+\hat{k}$, $\hat{\mathrm{i}}+\hat{\mathrm{j}}+\mu \hat{\mathrm{k}}$ are co-planer, is :
2
0
-1
1
Correct Option: , 3
Solution:
$\left|\begin{array}{ccc}\mu & 1 & 1 \\ 1 & \mu & 1 \\ 1 & 1 & \mu\end{array}\right|=0$
$\mu\left(\mu^{2}-1\right)-1(\mu-1)+1(1-\mu)=0$
$\mu^{3}-\mu-\mu+1+1 \mu=0$
$\mu^{3}-3 \mu+2=0$
$\mu^{3}-1-3(\mu-1)=0$
$\mu=1, \mu^{2}+\mu-2=0$
$\mu=1, \mu=-2$
sum of distinct solutions $=-1$
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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,
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