Introduction to QuaternionsMacmillan and Company, 1882 - 232 |
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Strona 37
... Vaß , where S is read scalar , V vector : and we find Saẞ - TaTẞ cos 0 , Vaẞ TaTẞe sin 0 . € = 4. The coefficient of e in Vaß is the area of the parallelogram whose sides are equal and parallel to the lines of which a , ẞ are the ...
... Vaß , where S is read scalar , V vector : and we find Saẞ - TaTẞ cos 0 , Vaẞ TaTẞe sin 0 . € = 4. The coefficient of e in Vaß is the area of the parallelogram whose sides are equal and parallel to the lines of which a , ẞ are the ...
Strona 38
... Vaß is a vector in the direction perpendicular to the plane which passes through a , ß . 9. a2ßaß . Ba because ẞ is a scalar ; .. a2ß3 = ( Saß + Vaß ) ( Saß – Vaß ) = ( Saẞ ) - ( Vaẞ ) " . Note . a3ß2 must not be confounded with ( aß ) ...
... Vaß is a vector in the direction perpendicular to the plane which passes through a , ß . 9. a2ßaß . Ba because ẞ is a scalar ; .. a2ß3 = ( Saß + Vaß ) ( Saß – Vaß ) = ( Saẞ ) - ( Vaẞ ) " . Note . a3ß2 must not be confounded with ( aß ) ...
Strona 40
... Vaß and VyAH = -Vyd = Vdy ( 22. 2 ) , V ( a + y ) AH = Vaß + Vdy , i . e . ( 21. 4 ) , the parallelogram whose sides are parallel and equal to BC , AH , equals the two parallelograms whose sides are parallel and equal to BA , AE ; GA ...
... Vaß and VyAH = -Vyd = Vdy ( 22. 2 ) , V ( a + y ) AH = Vaß + Vdy , i . e . ( 21. 4 ) , the parallelogram whose sides are parallel and equal to BC , AH , equals the two parallelograms whose sides are parallel and equal to BA , AE ; GA ...
Strona 55
... Vaẞ = y ' ( 21. 3 ) , a vector perpendicular to the plane OAB ( fig . of formula 2 ) ; Vẞy = a , a vector perpendicular to the plane OBC ; and since y ' , a ' are both perpendicular to OB , the line along which is the vector ß ; OB is ...
... Vaẞ = y ' ( 21. 3 ) , a vector perpendicular to the plane OAB ( fig . of formula 2 ) ; Vẞy = a , a vector perpendicular to the plane OBC ; and since y ' , a ' are both perpendicular to OB , the line along which is the vector ß ; OB is ...
Strona 62
... ( Vaẞ + Vẞy + Vya ) – S. aßy = 0 is the equation required . Smel COR . Vaß + Vẞy + Vya is a vector in the direction perpen- dicular to the plane ; therefore ( No. 3 ) the perpendicular vector from the origin = S . aẞy . ( Vaẞ + Vßy + Vya ) ...
... ( Vaẞ + Vẞy + Vya ) – S. aßy = 0 is the equation required . Smel COR . Vaß + Vẞy + Vya is a vector in the direction perpen- dicular to the plane ; therefore ( No. 3 ) the perpendicular vector from the origin = S . aẞy . ( Vaẞ + Vßy + Vya ) ...
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A. S. WALPOLE A. W. VERRALL ALGEBRA ARITHMETIC Assistant Master aßy axis BEGINNERS bisects Cambridge centre chord circle cone CONIC SECTIONS conjugate diameters constant drawn Edited ELEMENTARY TREATISE ellipse ellipsoid ENGLISH equal EXAMPLES Exercises Fcap find the locus G. E. FASNACHT GEOMETRY given lines given point gives GRAMMAR GREEK Hence HISTORY hyperbola Illustrated intersection Introduction and Notes ISAAC TODHUNTER J. P. MAHAFFY LATIN Litt Litt.D LL.D M.A. BOOK M.A. Cr MACMILLAN'S Mathematics middle points parabola parallelepiped parallelogram PRIMER Prof Professor quaternion revised right angles rotation Sapa Saß scalar School shews Spop squares strain tangent plane tetrahedron Translated triangle Trinity College unit vectors values Vaß vector parallel vector perpendicular Vẞy whence yẞ αβγ φρ
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