vectors and scalars - 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, (e)Three vectors not lying in a plane can never add up to give a null vector.

Grigori (last edited 1 year ago) (Student, UG2 Grade)

a) True statement.

A vector's magnitude is a number. therefore, it is a scalar.

b) False statement.

Each vector component has its own magnitude and direction. As a result, it is a vector quantity.

c) False statement.

Displacement is a vector quantity, while total path length is a scalar quantity. As a result, the total path length is always greater than the displacement magnitude. And when a particle moves in a straight line it become equal to the magnitude of displacement.

d) True statement.

This is due to the fact that the total path length is often greater than or equal to the magnitude of a particle's displacement.

e) True statement.

Three vectors that do not lie in a plane cannot be described in the same order by the sides of a triangle.