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 $\theta _2$ ?

The resultant of $\vec A$ and $\vec B$ makes an angle $\alpha $ with $\vec A$ and $\beta $ with $\vec B$,

The value of the sum of two vectors $\overrightarrow A $ and $\overrightarrow B $ with $\theta $ as the angle between them is

$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. then $\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}=.......$

The magnitude of a given vector with end points $ (4, -4, 0)$ and $(-2, -2, 0)$ must be

Two forces $P$ and $Q$, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta $ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\theta $ is ....... $^o$