If $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ are two vectors satisfying the relation $\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}=|\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}|$. Then the value of $|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|$ will be :
$\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}}$
$\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+\sqrt{2} \mathrm{AB}}$
$\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}+2 \mathrm{AB}}$
$\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}-\sqrt{2} \mathrm{AB}}$
Correct Option: , 4
$\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}=|\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}|$
$A B \cos \theta=A B \sin \theta \Rightarrow \theta=45^{\circ}$
$|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|=\sqrt{\mathrm{A}^{2}+\mathrm{B}^{2}-2 \mathrm{AB} \cos 45^{\circ}}$
Hence option (4).
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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,