Question

The translational distances $(dx,dy)$ is called
A.Translational vector
B.Shift vector
C.Both A and B
D.Neither A nor B

Answer 1

The words translation vector and shift vector point towards the same thing, they mean the vectors that are shifted in the coordinate plane without rotating. $(dx,dy)$ are the infinitely small distances of $(x,y)$ in magnitude and have the same direction as $(x,y)$.

Complete step by step answer:
Translational vectors or shift vectors are the vectors which can be shifted/ translated/ moved in the plane from one place to another. But they can only move or slide parallelly to their original position and cannot be rotated at all. Here the translational distances $(dx,dy)$ are the derivatives or differential form of distances $(x,y)$ point on the coordinate plane. Therefore, the displacement vector lies in the $xy -$plane and the body moves only in direction.
Additional info: An example of translatory motion can be a body moving uniformly along the $x -$axis in a straight line, here the body moves in the same direction therefore it can be termed as translatory motion. Translatory motion can be categorized into two: rectilinear and curvilinear. In a rectilinear translatory motion all the particles of the body move in the same direction, for example: a car moving in one direction, while in a curvilinear translatory motion the body moves along a curved path but exhibits translatory motion, for example: a car taking a turn.
The correct option is (C) Both A and B.

Note:
The question asks about translational distance i.e., the displacement takes place only in one dimension, from which we can conclude that the motion is not rotatory, therefore the correction option should be both translation vector and shift vectors as they also do not rotate.