The unit vector along $\hat i + \hat j$ is

- A
$\hat k$

- B
$\hat i + \hat j$

- C
$\frac{{\hat i + \hat j}}{{\sqrt 2 }}$

- D
$\frac{{\hat i + \hat j}}{2}$

Any vector in an arbitrary direction can always be replaced by two (or three)

The position vector of a particle is $\vec r = (a\cos \omega t)\hat i + (a\sin \omega t)\hat j$. The velocity of the particle is

- [AIPMT 1995]

A particle starting from the origin $(0, 0)$ moves in a straight line in the $(x, y)$* *plane. Its coordinates at a later time are $(\sqrt 3 , 3) .$ The path of the particle makes with the $x-$axis an angle of ......... $^o$

- [AIPMT 2007]

The expression $\left( {\frac{1}{{\sqrt 2 }}\hat i + \frac{1}{{\sqrt 2 }}\hat j} \right)$ is a

Surface area is