The angle between vectors $\vec a$ and $\vec b$ is $\frac{\pi }{6}$. The angle between vectors $ – 3\vec a$ and $ 2\vec b$ is

“Explain the meaning of multiplication of vectors by real numbers with an example.”

A particle is moving with speed $6\,m/s$ along the direction of  $\vec A = 2\hat i + 2\hat j – \hat k,$ then its velocity 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.

If $\vec P = \vec Q$ then which of the following is NOT correct