A person moves $30\, m$ north and then $20\, m$ towards east and finally $30\sqrt 2 \,m$  in south-west direction. The displacement of the person from the origin will be

A particle is moving eastwards with a speed of $6 \,m / s$. After $6 \,s$, the particle is found to be moving with same speed in a direction $60^{\circ}$ north of east. The magnitude of average acceleration in this interval of time is ....... $m / s ^2$

$List I$ describes four systems, each with two particles $A$ and $B$ in relative motion as shown in figure. $List II$ gives possible magnitudes of then relative velocities (in $ms ^{-1}$ ) at time $t=\frac{\pi}{3} s$.

Which one of the following options is correct?

What can be the angle between velocity and acceleration for the motion in two or three dimension ?

and direction of the vectors $\hat{ i }+\hat{ j }$, and $\hat{ i }-\hat{ j }$ ? What are the components of a vector $A =2 \hat{ i }+3 \hat{ j }$ along the directions of $\hat{ i }+\hat{ j }$ and $\hat{ i }-\hat{ j } ?$

Give examples of one dimensional, two dimensional and three dimensional motion.