If the angle between $\hat a$ and $\hat b$ is $60^o$, then which of the following vector $(s)$ have magnitude one
$(A)$ $\frac{\hat a + \hat b}{\sqrt 3}$ $(B)$ $\hat a + \widehat b$ $(C)$ $\hat a$ $(D)$ $\hat b$
Only $C,D$
Only $B,C,D$
Only $A,C,D$
All
Two equal forces ($P$ each) act at a point inclined to each other at an angle of $120^°$. The magnitude of their resultant is
Which of the following is independent of the choice of co-ordinate system
On an open ground, a motorist follows a track that turns to his left by an angle of $60^{°}$ after every $500\; m$. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.