The resultant of two vectors at an angle $150^{\circ}$ is $10$ units and is perpendicular to one vector. The magnitude of the smaller vector is ....... units

In the cube of side $a$ shown in the figure, the vector from the central point of the face $ABOD$ to the central point of the face $BEFO$ will be

The coordinates of a moving particle at any time $t$ are given by $x = a\, t^2$ and $y = b\, t^2$. The speed of the particle is

A scooter going due east at $10\, ms^{-1}$ turns right through an angle of $90^°$. If the speed of the scooter remains unchanged in taking turn, the change is the velocity of the scooter is

The resultant of $\overrightarrow A + \overrightarrow B $ is ${\overrightarrow R _1}.$ On reversing the vector $\overrightarrow {B,} $ the resultant becomes ${\overrightarrow R _2}.$ What is the value of $R_1^2 + R_2^2$

The resultant of these forces $\overrightarrow{O P}, \overrightarrow{O Q}, \overrightarrow{O R}, \overrightarrow{O S}$ and $\overrightarrow{{OT}}$ is approximately $\ldots \ldots {N}$.

[Take $\sqrt{3}=1.7, \sqrt{2}=1.4$ Given $\hat{{i}}$ and $\hat{{j}}$ unit vectors along ${x}, {y}$ axis $]$