Explain the parallelogram method for vector addition. Also explain that this is comparable to triangle method.
Explain the parallelogram method for vector addition. Also explain that this is comparable to triangle method.
$\vec{A}$ and $\vec{B}$ are to be added as shown in figure $(a).$
Select a point $\mathrm{O}$ as shown in figure $(b)$.
Represent $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$ such that their lengths and directions remain unchanged and their tails remain at $\mathrm{O}$.
Draw a parallelogram $\square^{\mathrm{m}}$ OPSQ in which $\vec{A}$ and $\vec{B}$ are adjacent sides of it. Draw a diagonal OS from $\mathrm{O}$.
Vector $\overrightarrow{\mathrm{OS}}$ represent resultant vector of addition of $\overrightarrow{\mathrm{A}}$ and $\overrightarrow{\mathrm{B}}$.
$\overrightarrow{\mathrm{OS}}=\overrightarrow{\mathrm{OP}}+\overrightarrow{\mathrm{OQ}} \quad \therefore \overrightarrow{\mathrm{R}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}$
Triangle method for vector addition is shown in figure $(c)$.
If is clear that both methods give equal resultant vector. Hence, both methods are comparable to each other.
Here, magnitude of resultant vector $\overrightarrow{\mathrm{R}},|\overrightarrow{\mathrm{R}}| \leq|\overrightarrow{\mathrm{A}}|+|\overrightarrow{\mathrm{B}}|$
Similar Questions
Two forces of $12 \,N$ and $8 \,N$ act upon a body. The resultant force on the body has maximum value of........$N$
Two forces of $12 \,N$ and $8 \,N$ act upon a body. The resultant force on the body has maximum value of........$N$
Assertion $A$ : If $A, B, C, D$ are four points on a semi-circular arc with centre at $'O'$ such that $|\overrightarrow{{AB}}|=|\overrightarrow{{BC}}|=|\overrightarrow{{CD}}|$, then $\overrightarrow{{AB}}+\overrightarrow{{AC}}+\overrightarrow{{AD}}=4 \overrightarrow{{AO}}+\overrightarrow{{OB}}+\overrightarrow{{OC}}$
Reason $R$ : Polygon law of vector addition yields $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{A D}=2 \overrightarrow{A O}$
In the light of the above statements, choose the most appropriate answer from the options given below
Assertion $A$ : If $A, B, C, D$ are four points on a semi-circular arc with centre at $'O'$ such that $|\overrightarrow{{AB}}|=|\overrightarrow{{BC}}|=|\overrightarrow{{CD}}|$, then $\overrightarrow{{AB}}+\overrightarrow{{AC}}+\overrightarrow{{AD}}=4 \overrightarrow{{AO}}+\overrightarrow{{OB}}+\overrightarrow{{OC}}$
Reason $R$ : Polygon law of vector addition yields $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{A D}=2 \overrightarrow{A O}$
In the light of the above statements, choose the most appropriate answer from the options given below
- [JEE MAIN 2021]
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