Two vectors of same magnitude act at a point. Twice the product of the magnitudes of two vectors is equal to the square of the magnitude of their resultant. The angle between the two vectors is (in $^{\circ}$)

If $\overrightarrow{A}$ is a vector with magnitude $(3, 4)$,show that the magnitude of its unit vector is $1$.

Given that $\overrightarrow A + \overrightarrow B + \overrightarrow C = 0$. Out of three vectors,two are equal in magnitude and the magnitude of the third vector is $\sqrt{2}$ times that of either of the two having equal magnitude. Then the angles between the vectors are given by:

If the angle between unit vectors $\hat{a}$ and $\hat{b}$ is $60^{\circ}$, which of the following vectors have a magnitude of $1$?
$(A)$ $\frac{\hat{a} + \hat{b}}{\sqrt{3}}$
$(B)$ $\hat{a} + \hat{b}$
$(C)$ $\hat{a}$
$(D)$ $\hat{b}$

If $|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|$,then the angle between vector $\vec{A}$ and $\vec{B}$ is: (in $^{\circ}$)

What is a unit vector? Explain.