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. . . . . .

Unit vector parallel to the resultant of vectors $\vec A = 4\hat i – 3\hat j$and $\vec B = 8\hat i + 8\hat j$ will be

Let $\overrightarrow C = \overrightarrow A + \overrightarrow B $ then

When $n$ vectors of different magnitudes are added, we get a null vector. Then the value of $n$ cannot be