Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are in the ratio $3:1.$ Which of the following relations is true

If the angle between $\hat a$ and $\hat b$ is $60^o$, then which of the following  vector $(s)$ have magnitude one

$(A)$ $\frac{\hat a + \hat b}{\sqrt 3}$     $(B)$ $\hat a + \widehat b$     $(C)$ $\hat a$      $(D)$ $\hat b$

A particle is moving along a circular path with a constant speed of $10\,ms^{-1}.$ What is the magnitude of the change in velocity of the particle, when it moves through an angle of $60^{o}$ around the centre of the circle .......... $m/s$

A plane is revolving around the earth with a speed of $100\, km/hr $ at a constant height from the surface of earth. The change in the velocity as it travels half circle is.........$km/hr$

Unit vector parallel to the resultant of vectors $\vec A = 4\hat i - 3\hat j$and $\vec B = 8\hat i + 8\hat j$ will be

If $\vec{P}+\vec{Q}=\overrightarrow{0}$, then which of the following is necessarily true?