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By Ian O. Angell (auth.)

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This is the first time we have come ac ross the dual interpretation of a vector. We have used a vector as a means of uniquely determining a point in three-dimensional space; but it mayaiso be considered as a general direction, namely any line parallel to the line joining the origin to the point vector (as interpreted above). Of course, we move along a line in one of two possible directions, and so we need to define the sense of a direction vector, namely that from the origin towards the point vector in space; the opposite sense is obviously from the point towards the origin.

For if 8 x, 8 y, 8 z are the angles that such a directional vector makes with the respective positive x, Y and z-axes then the ratios d, :d2 :d 3 = cos 8 x : cos 8y : cos 8 z We know from the properties of three-dimensional geometry that cos 2 8 x + cos 2 8 y + cos 2 8 z = 1 Hence if the directional vector has modulus 1, then the coordinates of this vector must be (cos 8x , cos 8y , cos 8z ); these coordinates are called the direction eosines of the set of lines generated by the directional vector.

Sophisticated packages based on this very elementary idea are proving to be of great value in the electronic and engineering ind ustries. A variation on thi~ theme is the draw-drag-delete type of program. The idea is that the program contains aseries of subroutines, each of which can draw an elementary figure (such as a diagrammatic picture of an electronic component) relative to a reference point. The program can draw any number of these figures on the screen (and in this way a complete electronic circuit can be designed).

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