The figure shows three vectors $\vec{a}, \vec{b}$ and $\vec{c}$,where $R$ is the midpoint of $PQ$. Which of the following relations is correct?

Write two properties of vector addition.

The sum of the magnitudes of two vectors acting at a point is $18$ and the magnitude of their resultant is $12$. If the resultant is at $90^{\circ}$ with the vector of smaller magnitude,then the magnitudes of the vectors are

$A$ football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:

Two vectors $\vec{A}$ and $\vec{B}$ are defined as $\vec{A} = a \hat{i}$ and $\vec{B} = a(\cos \omega t \hat{i} + \sin \omega t \hat{j})$,where $a$ is a constant and $\omega = \pi / 6 \text{ rad s}^{-1}$. If $|\vec{A} + \vec{B}| = \sqrt{3}|\vec{A} - \vec{B}|$ at time $t = \tau$ for the first time,the value of $\tau$,in seconds,is . . . . . .

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