“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.
Similar Questions
Explain commutative law for vector addition.
Explain commutative law for vector addition.
The value of the sum of two vectors $\overrightarrow A $ and $\overrightarrow B $ with $\theta $ as the angle between them is
The value of the sum of two vectors $\overrightarrow A $ and $\overrightarrow B $ with $\theta $ as the angle between them is
Given below in Column $-I$ are the relations between vectors $\vec a \,$ $\vec b \,$ and $\vec c \,$ and in Column $-II$ are the orientations of $\vec a$, $\vec b$ and $\vec c$ in the $XY-$ plane. Match the relation in Column $-I$ to correct orientations in Column $-II$.
Column $-I$
Column $-II$
$(a)$ $\vec a \, + \,\,\vec b \, = \,\,\vec c $
$(i)$ Image
$(b)$ $\vec a \, - \,\,\vec c \, = \,\,\vec b$
$(ii)$ Image
$(c)$ $\vec b \, - \,\,\vec a \, = \,\,\vec c $
$(iii)$ Image
$(d)$ $\vec a \, + \,\,\vec b \, + \,\,\vec c =0$
$(iv)$ Image
Given below in Column $-I$ are the relations between vectors $\vec a \,$ $\vec b \,$ and $\vec c \,$ and in Column $-II$ are the orientations of $\vec a$, $\vec b$ and $\vec c$ in the $XY-$ plane. Match the relation in Column $-I$ to correct orientations in Column $-II$.
| Column $-I$ | Column $-II$ |
| $(a)$ $\vec a \, + \,\,\vec b \, = \,\,\vec c $ | $(i)$ Image |
| $(b)$ $\vec a \, - \,\,\vec c \, = \,\,\vec b$ | $(ii)$ Image |
| $(c)$ $\vec b \, - \,\,\vec a \, = \,\,\vec c $ | $(iii)$ Image |
| $(d)$ $\vec a \, + \,\,\vec b \, + \,\,\vec c =0$ | $(iv)$ Image |
Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $‘n’$ times the magnitude of $(\vec A - \vec B)$. The angle between $ \vec A$ and $\vec B$ is
Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $‘n’$ times the magnitude of $(\vec A - \vec B)$. The angle between $ \vec A$ and $\vec B$ is
- [JEE MAIN 2021]