Prove the associative law of vector addition.
Consider the vectors of shown in the figure. To find the associative law of $\vec{A}, \vec{B}$ and $\vec{C}$ Draw $\vec{A}=\overrightarrow{O P}, \vec{B}=\overrightarrow{P Q}$ and $\vec{C}=\overrightarrow{Q R}$
By triangle law of vector we get, Figure $(b)$
From the figure $\Delta \mathrm{OPQ}$
$\rightarrow \quad \rightarrow \quad \rightarrow \quad \rightarrow$
$\mathrm{A}+\mathrm{B}=\mathrm{OP}+\mathrm{PQ}$
$\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{OQ}}$
By adding $\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{QR}}$ in both the sides
$(\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}})+\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{OQ}}+\overrightarrow{\mathrm{QR}}$
We get $\quad(\vec{A}+\vec{B})+\vec{C}=\overrightarrow{O R} \ldots \ldots$ $(i)$
If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$ then magnitude and direction of $\overrightarrow A \, + \overrightarrow B $ will be
If $\overrightarrow R$ is the resultant vector of two vectors $\overrightarrow A $ and $\overrightarrow B $, then $\overrightarrow {\left| R \right|} \,...\,\overrightarrow {\left| A \right|} \, + \,\overrightarrow {\left| B \right|} $.
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 $\theta _2$ ?
“Explain Triangle method (head to tail method) of vector addition.”
If $|\,\vec A + \vec B\,|\, = \,|\,\vec A\,| + |\,\vec B\,|$, then angle between $\vec A$ and $\vec B$ will be ....... $^o$