By using properties of determinants, show that:
$\left|\begin{array}{lll}0 & a & -b \\ -a & 0 & -c \\ b & c & 0\end{array}\right|=0$
We have,
$\Delta=\left|\begin{array}{lll}0 & a & -b \\ -a & 0 & -c \\ b & c & 0\end{array}\right|$
Applying $\mathrm{R}_{1} \rightarrow c \mathrm{R}_{1}$, we have:]
$\Delta=\frac{1}{c}\left|\begin{array}{lll}0 & a c & -b c \\ -a & 0 & -c \\ b & c & 0\end{array}\right|$
Applying $\mathrm{R}_{1} \rightarrow \mathrm{R}_{1}-b \mathrm{R}_{2}$, we have:
$\begin{aligned} \Delta &=\frac{1}{c}\left|\begin{array}{lll}a b & a c & 0 \\ -a & 0 & -c \\ b & c & 0\end{array}\right| \\ &=\frac{a}{c}\left|\begin{array}{lll}b & c & 0 \\ -a & 0 & -c \\ b & c & 0\end{array}\right| \end{aligned}$
Here, the two rows R1 and R3 are identical.
$\therefore \Delta=0$.
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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,