Analytic Geometry of Space
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B. - A2B, (13) 20 PLANES AND LINES [Chap. IL The denominators in these expressions are, therefore, proportional to the direction cosines. In many problems, they may be used instead of the direction cosines themselves, but, in any case, the actual cosines may be determined by dividing these denominators by the square root of the sum of their squares. It should be observed that the equations of a line are not sufficient to deter- mine a positive direction on it.
19. Forms of the equations of a li...ne. If A, /u, v are the direction cosines of a line, and if P, ={xi, y^, Zj) is any point on it, the distance d from Pj to another point P = (x, y, z) on the line satis- fies the relations (Art. 4) Xd = X — Xi, fxd = y — yi, vd = z — z^. By eliminating d, we obtain the equations \ fJi V which are called the symmetric form of the equations of the line. Instead of the direction cosines themselves, it is frequently convenient to use, in these equations, three numbers a, b, c, pro- portional, respectively, to A, /a, v.
What to read after Analytic Geometry of Space?
You can find similar books in the "Read Also" column, or choose other free books by Virgil Snyder to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
B. - A2B, (13) 20 PLANES AND LINES [Chap. IL The denominators in these expressions are, therefore, proportional to the direction cosines. In many problems, they may be used instead of the direction cosines themselves, but, in any case, the actual cosines may be determined by dividing these denominators by the square root of the sum of their squares. It should be observed that the equations of a line are not sufficient to deter- mine a positive direction on it.
19. Forms of the equations of a li...ne. If A, /u, v are the direction cosines of a line, and if P, ={xi, y^, Zj) is any point on it, the distance d from Pj to another point P = (x, y, z) on the line satis- fies the relations (Art. 4) Xd = X — Xi, fxd = y — yi, vd = z — z^. By eliminating d, we obtain the equations \ fJi V which are called the symmetric form of the equations of the line. Instead of the direction cosines themselves, it is frequently convenient to use, in these equations, three numbers a, b, c, pro- portional, respectively, to A, /a, v.
What to read after Analytic Geometry of Space?
You can find similar books in the "Read Also" column, or choose other free books by Virgil Snyder to read onlineMoreLess
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