Explain the commutative law for vector addition.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Consider two vectors $\vec{A}$ and $\vec{B}$. According to the parallelogram law of vector addition,we can construct a parallelogram $OPRQ$ where $\vec{OP} = \vec{A}$ and $\vec{OR} = \vec{B}$.
From the triangle law of vector addition in $\Delta OPQ$:
$\vec{A} + \vec{B} = \vec{OP} + \vec{PQ} = \vec{OQ} \quad \dots (i)$
From the triangle law of vector addition in $\Delta ORQ$:
$\vec{B} + \vec{A} = \vec{OR} + \vec{RQ} = \vec{OQ} \quad \dots (ii)$
Since $\vec{PQ} = \vec{OR} = \vec{B}$ and $\vec{RQ} = \vec{OP} = \vec{A}$ in a parallelogram,comparing equations $(i)$ and $(ii)$,we get:
$\vec{A} + \vec{B} = \vec{B} + \vec{A}$
This proves that vector addition is commutative.

Explore More

Similar Questions

$\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors of equal magnitudes and $\theta$ is the angle between them. The angle between $\overrightarrow{A}$ or $\overrightarrow{B}$ with their resultant is

$A$ vector of length $\ell$ is turned by an angle $\theta$. Find the change in the position vector of the tip.

If the square of the resultant of two forces of equal magnitude is equal to three times their product,then the angle between them is ........ $^o$.

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{R_1}$. If vector $\vec{B}$ is reversed,the resultant becomes $\vec{R_2}$. What is the value of $R_1^2 + R_2^2$?

$A$ car travels $6 \, km$ at an angle of $45^\circ$ north of east and then travels $4 \, km$ at an angle of $135^\circ$ north of east. How far is the final point from the starting point? What angle does the straight line joining its initial and final position make with the east?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo