## Elements of vector algebra |

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Page 1

Vectors will be printed in Clarendon, thus A,

regardless of direction, or their tensors (as they are called) will be denoted by the

same letters in Italics. Thus, A will be the tensor of A ;

Vectors will be printed in Clarendon, thus A,

**B**, etc., or n, r,**s**, etc., and their sizes,regardless of direction, or their tensors (as they are called) will be denoted by the

same letters in Italics. Thus, A will be the tensor of A ;

**B**, n will be the tensors of ... Page 3

If only A—

leave a certain non- vanishing angle, ... we call sum of A and

from ...

If only A—

**B**(equal tensors only), then making the vectors A,**B**coinitial will stillleave a certain non- vanishing angle, ... we call sum of A and

**B**and denote by**S=****A**+**B**a third vector**S**which runs from the beginning to the end of the chain, i.e.from ...

Page 4

V Fig. i. The above vectorial expression will be read :

as well have linked the two given vectors so that the end-point of

the origin of A, as shown in the lower part of Fig. 1. Then their sum, say

...

V Fig. i. The above vectorial expression will be read :

**B**added to A. But we mightas well have linked the two given vectors so that the end-point of

**B**=**B**' falls intothe origin of A, as shown in the lower part of Fig. 1. Then their sum, say

**S**', would...

Page 5

Then, 0a(38 being a parallelogram and

have the following construction of the sum of two coinitial vectors A,

Through a, the end-point of A, draw a parallel to

...

Then, 0a(38 being a parallelogram and

**S**= 0 -> ft one of its diagonals, we shouldhave the following construction of the sum of two coinitial vectors A,

**B**(Fig. 2) :Through a, the end-point of A, draw a parallel to

**B**, and through f3, the end-point...

Page 6

superfluous, and either of the above expressions can simply be written A+

a nil vector or simply nil,

superfluous, and either of the above expressions can simply be written A+

**B**+C or**B**+A + C, and so on. ... a polygon), plane or not, then the sum of these vectors isa nil vector or simply nil,

**S=A**+**B**+C+D=o, and therefore also A + C +**B**+D=o, etc.### What people are saying - Write a review

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### Common terms and phrases

antisymmetric operator AVBC axis C(AB CALIFORNIA LIBRARY cartesian chain coefficients colatitude collinear vectors components conjugate coplanar corresponding principal value cosine cubic equation CVBA cyclic permutation definition 27 denoted direction in space distributive operator distributive property dyads end-point equal equation equivalent euclidean expressed fact fully determined geometrical given vectors important formula instance know beforehand latter linear operator linear vector operator meaning non-coplanar operator ST operator XS ordinary algebraic ordinary scalar origin parallel parallelogram constructed particle perpendicular plane polar coordinates polynomials principal axes proved reader represented S=A+B scalar factor scalar multiplication scalar number scalar product scalarly scarcely necessary self-conjugate short symbols Similarly Simplified Method spherical triangle symmetrical dyadic symmetrical operator tensor ternary product third vector three vectors trinomial UNIVERSITY OF CALIFORNIA vanishes VAVBC vector A stretched vector addends vector addition Vector Algebra vector function vector method vector multiplication vector operand vector product vector sum volume