Question

dimension of displacement vector
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Answer 1

Answer:

To describe motion in two and three dimensions, we must first establish a coordinate system and a convention for the axes. We generally use the coordinates x, y, and z to locate a particle at point P(x, y, z) in three dimensions. If the particle is moving, the variables x, y, and z are functions of time (t):

x=x(t)y=y(t)z=z(t).x=x(t)y=y(t)z=z(t).

The position vector from the origin of the coordinate system to point P is →r(t).r→(t). In unit vector notation, introduced in Coordinate Systems and Components of a Vector, →r(t)r→(t) is

→r(t)=x(t)^i+y(t)^j+z(t)^k.r→(t)=x(t)i^+y(t)j^+z(t)k^.

(Figure) shows the coordinate system and the vector to point P, where a particle could be located at a particular time t. Note the orientation of the x, y, and z axes. This orientation is called a right-handed coordinate system (Coordinate Systems and Components of a Vector) and it is used throughout the chapter.



Figure 4.2 A three-dimensional coordinate system with a particle at position P(x(t), y(t), z(t)).

With our definition of the position of a particle in three-dimensional space, we can formulate the three-dimensional displacement. (Figure) shows a particle at time t1t1 located at P1P1 with position vector →r(t1).r→(t1). At a later time t2,t2, the particle is located at P2P2 with position vector →r(t2)r→(t2). The displacement vector Δ→