
Assertion :- Vector addition is commutative.
Reason :- ($\vec{A}$+ $\vec{B}$) $\ne $ ($\vec{B}$+ $\vec{A}$)
( a ) Both assertion and reason are correct and reason is the correct explanation for assertion.
( b ) Both assertion and reason are correct and reason is not the correct explanation for assertion.
( c ) Assertion is correct but the reason is incorrect.
( d ) Both assertion and reason are incorrect.
Answer
164.4k+ views
Hint:
In this question, we are given that the addition of a vector is commutative. And the commutative law says that in which order we add the terms doesn’t matter. That is x+y = y+x. We find the vector A + B is equal or not equal to vector B + A then we choose the correct option.
Complete step by step solution:
Consider that we have two vectors $\vec{A}$ and $\vec{B}$ and we suppose that these are in ‘n’ dimensions.
Therefore, we can write $\vec{A}$as
< ${{A}_{1}},{{A}_{2}},{{A}_{3}},.....................,{{A}_{n}}$> and
$\vec{B}$ can be written as
<${{B}_{1}},{{B}_{2}},{{B}_{3}},.....................,{{B}_{n}}$>
Now we can find out $\vec{A}$ + $\vec{B}$
That is $\vec{A}$ + $\vec{B}$ = < ${{A}_{1}}+{{B}_{1}},{{A}_{2}}+{{B}_{2}},{{A}_{3}}+{{B}_{3}},.....................,{{A}_{n}}+{{B}_{n}}$>
As all the ${{A}_{i}}'s$ and the ${{B}_{i}}'s$ are the real numbers, therefore we can write the above equation as
$\vec{A}$ + $\vec{B}$ = <${{B}_{1}}+{{A}_{1}},{{B}_{2}}+{{A}_{2}},{{B}_{3}}+{{A}_{3}},.....................,{{B}_{n}}+{{A}_{n}}$>
This can be called as $\vec{B}$+ $\vec{A}$
Since vector addition is commutative,
Therefore :- ($\vec{A}$+ $\vec{B}$) = ($\vec{B}$+ $\vec{A}$)
Hence, the assertion is correct but the reason is incorrect.
Thus, Option (C) is the correct answer.
Therefore, the correct option is C.
Note:
In this question, we have to add the two vectors. Students must keep in mind the basic properties of vectors and how these properties are implemented on vectors. Questions may be asked on other properties like additive, homogeneity etc.
In this question, we are given that the addition of a vector is commutative. And the commutative law says that in which order we add the terms doesn’t matter. That is x+y = y+x. We find the vector A + B is equal or not equal to vector B + A then we choose the correct option.
Complete step by step solution:
Consider that we have two vectors $\vec{A}$ and $\vec{B}$ and we suppose that these are in ‘n’ dimensions.
Therefore, we can write $\vec{A}$as
< ${{A}_{1}},{{A}_{2}},{{A}_{3}},.....................,{{A}_{n}}$> and
$\vec{B}$ can be written as
<${{B}_{1}},{{B}_{2}},{{B}_{3}},.....................,{{B}_{n}}$>
Now we can find out $\vec{A}$ + $\vec{B}$
That is $\vec{A}$ + $\vec{B}$ = < ${{A}_{1}}+{{B}_{1}},{{A}_{2}}+{{B}_{2}},{{A}_{3}}+{{B}_{3}},.....................,{{A}_{n}}+{{B}_{n}}$>
As all the ${{A}_{i}}'s$ and the ${{B}_{i}}'s$ are the real numbers, therefore we can write the above equation as
$\vec{A}$ + $\vec{B}$ = <${{B}_{1}}+{{A}_{1}},{{B}_{2}}+{{A}_{2}},{{B}_{3}}+{{A}_{3}},.....................,{{B}_{n}}+{{A}_{n}}$>
This can be called as $\vec{B}$+ $\vec{A}$
Since vector addition is commutative,
Therefore :- ($\vec{A}$+ $\vec{B}$) = ($\vec{B}$+ $\vec{A}$)
Hence, the assertion is correct but the reason is incorrect.
Thus, Option (C) is the correct answer.
Therefore, the correct option is C.
Note:
In this question, we have to add the two vectors. Students must keep in mind the basic properties of vectors and how these properties are implemented on vectors. Questions may be asked on other properties like additive, homogeneity etc.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

Atomic Structure - Electrons, Protons, Neutrons and Atomic Models

Displacement-Time Graph and Velocity-Time Graph for JEE

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Learn About Angle Of Deviation In Prism: JEE Main Physics 2025

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

NCERT Solutions for Class 11 Physics Chapter 1 Units and Measurements

Units and Measurements Class 11 Notes: CBSE Physics Chapter 1

NCERT Solutions for Class 11 Physics Chapter 2 Motion In A Straight Line

Motion in a Straight Line Class 11 Notes: CBSE Physics Chapter 2

Important Questions for CBSE Class 11 Physics Chapter 1 - Units and Measurement
