“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.
A person moved from $A$ to $B$ on a circular path as shown in figure. If the distance travelled by him is $60 \,m$, then the magnitude of displacement would be$.....\,m$ (Given $\left.\cos 135^{\circ}=-0.7\right)$
The magnitude of vector $\overrightarrow A ,\,\overrightarrow B $ and $\overrightarrow C $ are respectively $12, 5$ and $13$ units and $\overrightarrow A + \overrightarrow B = \overrightarrow C $ then the angle between $\overrightarrow A $ and $\overrightarrow B $ is
$\overrightarrow A \, = \,2\widehat i\, + \,3\widehat j + 4\widehat k$ , $\overrightarrow B \, = \widehat {\,i} - \widehat j + \widehat k$, then find their substraction by algebric method.
Give the names of two methods for vector addition. Write the law of parallogram for vector addition.
$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. then $\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}=.......$