“Explain Triangle method (head to tail method) of vector addition.”
“Explain Triangle method (head to tail method) of vector addition.”
Let us consider two vectors $\vec{A}$ and $\vec{B}$ that lie in a plane as shown in figure $(a)$.
The lengths of the line segments representing these vectors are proportional to the magnitude of the vectors.
To find the sum $\vec{A}+\vec{B}$, we place vector $\vec{B}$ so that its tail is at the head of the vector $\vec{A}$, as in figure (b).
Then we join the tail of $\overrightarrow{\mathrm{A}}$ to the head of $\overrightarrow{\mathrm{B}}$.
This line $\overrightarrow{O Q}$ represent a vector $\vec{R}$, that is the sum of the vectors $\vec{A}$ and $\vec{B}$.
Since, in this procedure of vector addition, vectors are arranged head to tail, this graphical method is called the head-to-tail method.
The two vectors and their resultant form three sides of a triangle, so this method is also known as triangle method of vector addition.
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The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\overrightarrow{\mathrm{A}}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is . . . . . .
- [JEE MAIN 2024]
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]