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 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.

(a) True

Explanation: The magnitude of a vector is always a scalar because magnitude is a numerical value.

(b) False

Explanation: Each component of a vector is not always a scalar. Component of a vector is the effect of the vector in a given direction. It is also a vector.

(c) False

Explanation: The total path length is not always equal to the magnitude of the displacement vector of a particle. It is only true for a motion in straight line where the distance is equal to the magnitude of displacement.

(d) True

Explanation: The average speed of a particle is either greater or equal to the magnitude of average velocity of the particle over the same interval of time. Speed is the ratio of distance travelled to the time taken. Velocity is the ratio of displacement of an object to the time taken. For a given path over a given time period, distance is always greater than or equal to the displacement of the object. Hence, speed is always greater than or equal to velocity. The equality condition occurs for a straight line.

(e) True

Explanation: Three vectors not lying in a plane can never add up to give a null vector. For the resultant to be a null vector, the three vectors should form a triangle. The three sides of a triangle necessarily lie on the same plane. Hence, the given statement is true.