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

Two vectors $A$ and $B$ inclined at angle $\theta$ have a resultant $R$ which makes an angle $\phi$ with $A$. If the directions of $A$ and B are interchanged and resultant will have the same

The ratio of maximum and minimum magnitudes of the resultant of two vector $\vec a$ and $\vec b$ is $3 : 1$. Now $| \vec a |$  is equal to

Given that; $A = B = C$. If $\vec A + \vec B = \vec C,$ then the angle between $\vec A$ and $\vec C$ is $\theta _1$. If $\vec A + \vec B+ \vec C = 0,$ then the angle between $\vec A$ and $\vec C$ is $\theta _2$. What is the relation between $\theta _1$ and $\theta _2$ ?

The coordinates of a moving particle at any time $t$ are given by $x = a\, t^2$ and $y = b\, t^2$. The speed of the particle is

  • [AIIMS 2012]

Three forces given by vectors $2 \hat{i}+2 \hat{j}, 2 \hat{i}-2 \hat{j}$ and $-4 \hat{i}$ are acting together on a point object at rest. The object moves along the direction