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 $^{\circ}$)?

Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are at an angle of $60^{\circ}$ with each other. Their resultant makes an angle of $45^{\circ}$ with $\overrightarrow{a}$. If $|\vec{b}|=2$ units,then $|\vec{a}|$ is

Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are in the ratio $3:1.$ Which of the following relations is true?

The magnitude of the vector sum of two forces $10 \ N$ and $6 \ N$ cannot be ......... $N$.

Two forces,$F_1$ and $F_2$,are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is

The speed of a particle changes from $\sqrt{5} \ m/s$ to $2\sqrt{5} \ m/s$ in a time $t$. If the magnitude of change in its velocity is $5 \ m/s$,the angle between the initial and final velocities of the particle is (in $^{\circ}$)