A car moves towards north at a speed of $54 \,km / h$ for $1 \,h$. Then it moves eastward with same speed for same duration. The average speed and velocity of car for complete journey is ..........

Magnitudes of two vector $\overrightarrow A $ and $\overrightarrow B $ are $4$ units and $3$ units respectively. If these vectors are $(i)$ in same direction $(\theta = 0^o).$ $(ii)$ in opposite direction $(\theta = 180^o)$, then give the magnitude of resultant vector.

Given $a+b+c+d=0,$ which of the following statements eare correct:

$(a)\;a, b,$ c, and $d$ must each be a null vector,

$(b)$ The magnitude of $(a+c)$ equals the magnitude of $(b+d)$

$(c)$ The magnitude of a can never be greater than the sum of the magnitudes of $b , c ,$ and $d$

$(d)$ $b + c$ must lie in the plane of $a$ and $d$ if $a$ and $d$ are not collinear, and in the line of a and $d ,$ if they are collinear ?

Add vectors $\overrightarrow{ A }, \overrightarrow{ B }$ and $\overrightarrow{ C }$ each having magnitude of $50$ unit and inclined to the $X$-axis at angles $45^{\circ}, 135^{\circ}$ and $315^{\circ}$ respectively.

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

$100$  coplanner forces each equal to  $10\,\,N$  act on a body. Each force makes angle $\pi /50$ with the preceding force. What is the resultant of the forces.......... $N$