Explain commutative law for vector addition.

Vedclass pdf generator app on play store
Vedclass iOS app on app store

Consider the vector $\vec{A}$ and $\vec{B}$. According to Parallelogram of vector addition we get the figure.

Here, $\overrightarrow{\mathrm{A}}=\overrightarrow{\mathrm{OP}}=\overrightarrow{\mathrm{RQ}} ; \overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{OR}}=\overrightarrow{\mathrm{PQ}}$

Draw a Parallelogram,

From $\Delta \mathrm{OPQ} \quad \overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{OP}}+\overrightarrow{\mathrm{PQ}}$

$\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{OQ}}$

From $\Delta$ $ORQ$ $\vec{B}+\vec{A}=\overrightarrow{O R}+\overrightarrow{R Q}$

$=\overrightarrow{\mathrm{PQ}}+\overrightarrow{\mathrm{OP}}[\because \overrightarrow{\mathrm{OR}}=\overrightarrow{\mathrm{PQ}} \text { and } \overrightarrow{\mathrm{RQ}}=\overrightarrow{\mathrm{OP}}]$

$\overrightarrow{\mathrm{B}}+\overrightarrow{\mathrm{A}}=\overrightarrow{\mathrm{OQ}} \ldots \text { (ii) }$

From $(i)$ and $(ii)$ we get,

$\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{B}}+\overrightarrow{\mathrm{A}}$

885-s58

Similar Questions

How many minimum number of non-zero vectors in different planes can be added to give zero resultant

When vector $\overrightarrow{ A }=2 \hat{ i }+3 \hat{ j }+2 \hat{ k }$ is subtracted from vector $\vec{B}$, it gives a vector equal to $2 \hat{j}$. Then the magnitude of vector $\vec{B}$ will be:

  • [JEE MAIN 2023]

Two forces $\vec{F}_1$ and $\vec{F}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec{F}_1$ and $\overrightarrow{\mathrm{F}}_2$ is $\cos ^{-1}\left(\frac{1}{\mathrm{n}}\right)$. The value of $|\mathrm{n}|$ is__________.

  • [JEE MAIN 2024]

$\overrightarrow A \, = \,2\widehat i\, + \,3\widehat j + 4\widehat k$ , $\overrightarrow B \, = \widehat {\,i} - \widehat j + \widehat k$, then find their substraction by algebric method.

A particle is simultaneously acted by two forces equal to $4\, N$ and $3 \,N$. The net force on the particle is