The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to vector $\vec{A}$,and the resultant magnitude is equal to half of the magnitude of $\vec{B}$. Then,the angle between $\vec{A}$ and $\vec{B}$ is: (in $^{\circ}$)

An object is subjected to a force in the north-east direction. To balance this force,a second force should be applied in the direction:

Read each statement below carefully and state with reasons,if it is true or false:
$(a)$ The magnitude of a vector is always a scalar.
$(b)$ Each component of a vector is always a scalar.
$(c)$ The total path length is always equal to the magnitude of the displacement vector of a particle.
$(d)$ The average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time.
$(e)$ Three vectors not lying in a plane can never add up to give a null vector.

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

There are two vectors $\vec{A} = 6\hat{i} + 9\hat{j} - \hat{k}$ and $\vec{B} = 2\hat{i} + 3\hat{j} - p\hat{k}$ which have the same direction. The value of '$p$' is

The cosine values of the angles made by the vector $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ with the $X$,$Y$,and $Z$ axes respectively are: