TRANSFORMATION OF A VECTOR

Let v be a vector with the components

TRANSFORMATION OF A VECTOR

The component of vai in the direction of xb. is vai cos (6a) where ()a denotes the angle between 0bxb, and 0axai (see Fig. 4.10). Thus by adding the three components of va. in the direction of xb. we get

з

% = I la% i = 1 • • • 3

3=1

(4.4,1)

where

l.. = cos (0„.)

(4.4,2)

are the nine

direction cosines. Equation (4.4,1) is

evidently the matrix

product

(«)

where

ha = Ы Ф)

(4.4,3)

Подпись: (4.4,4)
Подпись: where TRANSFORMATION OF A VECTOR

and constitutes the required transformation formula. Its inverse readily reverses the transformation to give

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