The five sides of a regular pentagon are represented by vectors $A _1, A _2, A _3, A _4$ and $A _5$, in cyclic order as shown below. Corresponding vertices are represented by $B _1, B _2, B _3, B _4$ and $B _5$, drawn from the centre of the pentagon.Then, $B _2+ B _3+ B _4+ B _5$ is equal to

How many minimum number of non-zero vectors in different planes can be added to give zero resultant

Which of the four arrangements in the figure correctly shows the vector addition of two forces $\overrightarrow {{F_1}} $ and $\overrightarrow {{F_2}} $ to yield the third force $\overrightarrow {{F_3}} $

Two forces are such that the sum of their magnitudes is $18\; N$ and their resultant is $12\; N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are

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. . . . . .