Page 13 - mechanics

Chapter – 3 Concurrent forces in 3D

In this chapter we generalize the ideas and the work, that be
handled in chapter two, in the three dimensions space 3D.
3.1 Rectangular Components of Vectors in Space

A point in plane can be completely identified by two
coordinate: one to indicate left or right and the other to indicate
above or below. That is why it is called two dimensions and
usually abbreviated as 2D. Yet, in the case of space, a third
number is needed to indicate the depth of the point. That is
why it is called three dimensions and abbreviated as 3D.

The same concept applies to vector. A Cartesian vector
form in 2D has only two components. It can be anticipated that
in 3D a vector has three components; the usual two of a plane
and the third one for the depth.

From the perpendicularity of the three Cartesian coordinate
axes x, y and z, it is obvious that z axis is perpendicular to the
xy plane and y axis is perpendicular to xz plane and x axis is
perpendicular to yz plane. Thus, consider a general vector in
3D and carrying out vector resolution into two perpendicular
components. Choose one of the two components on the z axis,
the other perpendicular component thus lies definitely in the
xy plane A = A' + Az

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