If $\left| {{{\vec v}_1} + {{\vec v}_2}} \right| = \left| {{{\vec v}_1} - {{\vec v}_2}} \right|$ and ${{{\vec v}_1}}$ and ${{{\vec v}_2}}$ are finite, then

Give the names of two methods for vector addition. Write the law of parallogram for vector addition.

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 .......

Two forces ${F_1} = 1\,N$ and ${F_2} = 2\,N$ act along the lines $x = 0$ and $y = 0$ respectively. Then the resultant of forces would be

The magnitude of vector $\overrightarrow A ,\,\overrightarrow B $ and $\overrightarrow C $ are respectively $12, 5$ and $13$ units and $\overrightarrow A + \overrightarrow B = \overrightarrow C $ then the angle between $\overrightarrow A $ and $\overrightarrow B $ is