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

Two forces of magnitude $8 \,N$ and $15 \,N$ respectively act at a point. If the resultant force is $17 \,N$, the angle between the forces has to be .......

Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the forces  Also name the triangle formed by the forces as sides

If $\vec{P}+\vec{Q}=\overrightarrow{0}$, then which of the following is necessarily true?

Given that $\vec A\, + \,\vec B\, = \,\vec C\,.$  If  $\left| {\vec A} \right|\, = \,4,\,\,\left| {\vec B} \right|\, = \,5\,\,$ and $\left| {\vec C} \right|\, =\,\sqrt {61}$ the angle between $\vec A\,\,$ and $\vec B$ is ....... $^o$

Which of the following relations is true for two unit vectors $\hat{ A }$ and $\hat{ B }$ making an angle $\theta$ to each other$?$