Position of a particle in a rectangular-co-ordinate system is $(3, 2, 5)$. Then its position vector will be

State, for each of the following physical quantities, if it is a scalar or a vector : volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.

If $\overrightarrow A $ is $(3,\, 4)$ unit, then show that the value of its unit vector is $1$.

A vector is represented by $3\,\hat i + \hat j + 2\,\hat k$. Its length in $XY$ plane is

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.

What is unit vector ? Explain.