What should be the angle $\theta$ between two vectors $\vec{A}$ and $\vec{B}$ so that the magnitude of the resultant vector $\vec{R}$ is maximum (in $^{\circ}$)?

The resultant of two vectors $A$ and $B$ makes an angle $\alpha$ with $A$ and $\beta$ with $B$. Which of the following is correct?

$ABC$ is an equilateral triangle. The length of each side is $a$ and the centroid is point $O$. Then $\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC} = \dots$

If $|\vec{v}_1 + \vec{v}_2| = |\vec{v}_1 - \vec{v}_2|$ and $\vec{v}_1$ and $\vec{v}_2$ are finite,then:

Can the resultant of three vectors of unequal magnitudes be a zero vector?

$A$ vector has a magnitude the same as that of $\overrightarrow{A} = 3 \hat{i} + 4 \hat{j}$ and is parallel to $\overrightarrow{B} = 4 \hat{i} + 3 \hat{j}$. The $x$ and $y$ components of this vector in the first quadrant are $X$ and $3$ respectively,where $X = $ . . . . . . .