The value of a unit vector in the direction of vector $\vec A = 5\hat i - 12\hat j$ is:

If $\alpha, \beta$ and $\gamma$ are the angles made by a vector with $x, y$ and $z$ axes respectively,then $\sin ^2 \alpha + \sin ^2 \beta =$

Define scalar and vector physical quantities with their examples.

If $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$,then the angle between $\vec{A}$ and $\vec{B}$ is ........ $^\circ$.

If a particle moves from point $P (2, 3, 5)$ to point $Q (3, 4, 5)$,its displacement vector is:

$A$ vector $\vec{A}$ is rotated by a small angle $\Delta \theta$ radian $(\Delta \theta \ll 1)$ to get a new vector $\vec{B}$. In that case,$|\vec{B} - \vec{A}|$ is