Two vectors $\overrightarrow{\mathrm{X}}$ and $\overrightarrow{\mathrm{Y}}$ have equal magnitude. The magnitude of $(\vec{X}-\vec{Y})$ is $n$ times the magnitude of $(\overrightarrow{\mathrm{X}}+\overrightarrow{\mathrm{Y}})$. The angle between $\overrightarrow{\mathrm{X}}$ and $\overrightarrow{\mathrm{Y}}$ is :
$\cos ^{-1}\left(\frac{-n^{2}-1}{n^{2}-1}\right)$
$\cos ^{-1}\left(\frac{n^{2}-1}{-n^{2}-1}\right)$
$\cos ^{-1}\left(\frac{n^{2}+1}{-n^{2}-1}\right)$
$\cos ^{-1}\left(\frac{n^{2}+1}{n^{2}-1}\right)$
Correct Option: , 2
Given $\mathrm{X}=\mathrm{Y}$
$\sqrt{\mathrm{X}^{2}+\mathrm{Y}^{2}-2 \times \mathrm{Y} \cos \theta}$
$=n \sqrt{X^{2}+Y^{2}+2 \times Y \cos \theta}$
Square both sides
$2 \mathrm{X}^{2}(1-\cos \theta)=\mathrm{n}^{2} \cdot 2 \mathrm{X}^{2}(1+\cos \theta)$
$1-\cos \theta=n^{2}+n^{2} \cos \theta$
$\cos \theta=\frac{1-\mathrm{n}^{2}}{1+\mathrm{n}^{2}}$
$\theta=\cos ^{-1}\left[\frac{n^{2}-1}{-n^{2}-1}\right]$
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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,