By J. Gibbs
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Extra info for Vector Analysis
Example text
1 l = I and V PA _ JL-1 PA* ZZ ~~& 7 . WC = A =B+ Equating BA D, B and C coplanar with in of be terms them. may expressed is it 7i +m+n " ^7 as the A P be BD VECTOR ANALYSIS 26 A B = # 2 C + y2 D A B = ^t + B B = B + & 2 (P - B). PL CC* 3D the four ratios the result i that d JL vn No scale of num bers can represent them adequately. It can represent only their magnitude, not their direction. ] Definition : A vector is a quantity which is considered as possessing direction as well as magnitude. Definition : A scalar is a quantity which is considered as pos sessing magnitude but no direction. VECTOR ANALYSIS 2 The positive and negative numbers of ordinary algebra are the For this reason the ordinary algebra is called typical scalars. scalar algebra when necessary to distinguish it from the vector algebra or analysis which the subject of this book. It since ED is by hypothesis paral the equation The sum should be. =n (C - B) of the coefficients Rearrange the is evidently zero as terms so that the equation takes on the form E nC = "D 7i B. The vector E n C is coplanar with E and C. It must cut the line EC. The equal vector D 7&B is coplanar with D and B. It must cut the line DB. Consequently the vector represented by either side of this equation must pass through the point A. iB = #A.