Given that $\vec{A} + \vec{B} = \vec{C}$. If $|\vec{A}| = 4, |\vec{B}| = 5$ and $|\vec{C}| = \sqrt{61}$,the angle between $\vec{A}$ and $\vec{B}$ is ....... $^o$

Which of the four arrangements in the figure correctly shows the vector addition of two forces $\overrightarrow {{F_1}} $ and $\overrightarrow {{F_2}} $ to yield the third force $\overrightarrow {{F_3}} $?

The figure shows three vectors $p$,$q$,and $r$,where $C$ is the midpoint of $AB$. Which of the following relations is correct?

The vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$. The angle between the two vectors is: (in $^{\circ}$)

Two forces $\vec{F}_1$ and $\vec{F}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec{F}_1$ and $\vec{F}_2$ is $\cos^{-1}\left(\frac{1}{n}\right)$. The value of $|n|$ is . . . . . . .

If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$,find the magnitude and direction of $\overrightarrow A + \overrightarrow B$.