In an octagon $A B C D E F G H$ of equal side, what is the sum of
$-16 \hat{\mathrm{i}}-24 \hat{\mathrm{j}}+32 \hat{\mathrm{k}}$
$16 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}-32 \hat{\mathrm{k}}$
$16 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}+32 \hat{\mathrm{k}}$
$16 \hat{\mathrm{i}}-24 \hat{\mathrm{j}}+32 \hat{\mathrm{k}}$
Correct Option: , 2
We know,
By triangle law of vector addition, we can write
Now
$\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{AD}}+\overrightarrow{\mathrm{AE}}+\overrightarrow{\mathrm{AF}}+\overrightarrow{\mathrm{AG}}+\overrightarrow{\mathrm{AH}}$
$=(7 \overrightarrow{\mathrm{AO}})+\overrightarrow{\mathrm{OB}}+\overrightarrow{\mathrm{OC}}+\overrightarrow{\mathrm{OD}}+\overrightarrow{\mathrm{OE}}+\overrightarrow{\mathrm{OF}}+\overrightarrow{\mathrm{OG}}+\overrightarrow{\mathrm{OH}}$
$=(7 \overrightarrow{\mathrm{AO}})+\overrightarrow{0}-\overrightarrow{\mathrm{OA}}$
$=(7 \overrightarrow{\mathrm{AO}})+\overrightarrow{\mathrm{AO}}$
$=8 \overrightarrow{\mathrm{AO}}=8(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}})$
$=16 \hat{\mathrm{i}}+24 \hat{\mathrm{j}}-32 \hat{\mathrm{k}}$
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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,