By Henry G. Booker

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7(a) were varied, a corresponding variation would occur in the magnitude and direction of the vector a±s in Fig. 7(b), and consequently in the resultant vector P. In this way we can calculate for the vector P defined by Eqs. 35) the way in which its magnitude and direction vary with the magnitude and direction of s. 42) Let us evaluate the magnitude and direction of the vector P denned by these equations when the vector s is given by »= 5^f (2-43) as illustrated in Fig. 8(a). To evaluate the vector on the right-hand side of Eq.

65). 2 »r\ (b) FIG. 12. Illlustrating verification of the root in Eq. 51) when the coefficients are given by Eqs. 65). 48 2. Vector Algebra Using Planar Products and Quotients 25. Relation between Vector Algebra and Scalar Algebra In the preceding section we have seen that the processes of vector algebra are closely related to the processes of scalar algebra provided that the operations of addition, subtraction, multiplication, and division are interpreted as addition, subtrac tion, planar multiplication, and division of vectors.

75). Quadrature direction J • -1 2 0 -j Reference direction (a) Quadrature direction j -1 0 -j- P 3 » m 4Ϊ S2 Reference " * " direction (b) FIG. 13. Illustrating (a) the vector s given by Eq. 79), and (b) calculation of the corresponding vector P given by Eq. 78). Corresponding to the negative value —2 for ί in Eq. 76), let us now consider a vector of magnitude 2 in the direction opposite to the reference direction, so that s = 2 /_π. 81) This situation is illustrated in Fig. 14, and we see that P = 1 z>.