(a) The magnitude of a vector is always a scalar.
Answer: True.
The magnitude of a vector is just a number representing its size or length, with no direction attached. Since scalars are quantities having only magnitude and no direction, the magnitude of a vector is a scalar.
(b) Each component of a vector is always a scalar.
Answer: False.
Each component (e.g. \( A_x, A_y, A_z \)) is a scalar number, but when we talk of the component along an axis as a vector, it has both magnitude and direction (along that axis). So numerically the components are scalars, but the component vectors themselves are vectors; the statement is ambiguous and taken as false in this context.
(c) The total path length is always equal to the magnitude of the displacement vector of a particle.
Answer: False.
Displacement is the straight-line vector from initial to final position, whereas total path length is the actual distance travelled along the trajectory. For curved or zig-zag paths, path length > displacement; they are equal only if motion is along a straight line in one direction.
(d) The average speed of a particle (total path length divided by time) is either greater or equal to the magnitude of average velocity over the same time interval.
Answer: True.
Average speed uses total path length, while average velocity uses displacement, whose magnitude is ≤ path length. Dividing both by the same time gives average speed ≥ magnitude of average velocity, equality only for straight-line motion in one direction.
(e) Three vectors not lying in a plane can never add up to give a null vector.
Answer: True.
For three vectors to sum to zero, they must form the sides of a triangle head-to-tail, which is only possible if they lie in a single plane. If the three vectors are not coplanar, they cannot form a closed triangle, so their vector sum cannot be the null vector.