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

A boy walks uniformally along the sides of a rectangular park of size $400\, m × 300\, m$, starting from one corner to the other corner diagonally opposite. Which of the following statement is incorrect

What is unit vector ? Explain.

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.

State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful :

$(a)$ adding any two scalars,

$(b)$ adding a scalar to a vector of the same dimensions ,

$(c)$ multiplying any vector by any scalar,

$(d)$ multiplying any two scalars,

$(e)$ adding any two vectors,

$(f)$ adding a component of a vector to the same vector.

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