Introduction to Quaternions |
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Page 59
... origin 0 ; then AP is a vector parallel to ß and gives = xẞ , say , OP = 0A + AP p = a + xß ( 1 ) as the equation of the line . 2. Another form in which the equation of a straight line may be expressed is this : let OA = a , OB = ẞ be ...
... origin 0 ; then AP is a vector parallel to ß and gives = xẞ , say , OP = 0A + AP p = a + xß ( 1 ) as the equation of the line . 2. Another form in which the equation of a straight line may be expressed is this : let OA = a , OB = ẞ be ...
Page 61
... origin on a given line . Equation ( 1 ) of Art . 32 is If now we get or p = a + xß . p = OD = 8 ; SS2 = Ssa , - OD2 = Sda ; δα .. OD : = - OD = - Sa US , Ud being the unit vector perpendicular to the line . COR . The same result is true ...
... origin on a given line . Equation ( 1 ) of Art . 32 is If now we get or p = a + xß . p = OD = 8 ; SS2 = Ssa , - OD2 = Sda ; δα .. OD : = - OD = - Sa US , Ud being the unit vector perpendicular to the line . COR . The same result is true ...
Page 62
... origin = S . aẞy . ( Vaẞ + Vßy + Vya ) ̃ ' . 6. To find the equation of a plane which shall pass through a given point and be parallel to each of two given straight lines . منا γ Let be the vector to the given point , 62 [ CHAP . IV ...
... origin = S . aẞy . ( Vaẞ + Vßy + Vya ) ̃ ' . 6. To find the equation of a plane which shall pass through a given point and be parallel to each of two given straight lines . منا γ Let be the vector to the given point , 62 [ CHAP . IV ...
Page 63
... equations ( 2 ) and ( 3 ) is the condition necessary and sufficient for coplanarity . 9. To find the line of intersection of two planes through the origin . Let Sap = 0 , SBp = 0 be the ART . 34. ] 63 THE STRAIGHT LINE AND PLANE .
... equations ( 2 ) and ( 3 ) is the condition necessary and sufficient for coplanarity . 9. To find the line of intersection of two planes through the origin . Let Sap = 0 , SBp = 0 be the ART . 34. ] 63 THE STRAIGHT LINE AND PLANE .
Page 65
... origin . Here the axes are given , so that i , j , k are known unit vectors . Let ai , bj , ck be the portions cut off from the axes by a plane , the perpendicular on which from the origin is p . Then p - ai is perpendicular to p ...
... origin . Here the axes are given , so that i , j , k are known unit vectors . Let ai , bj , ck be the portions cut off from the axes by a plane , the perpendicular on which from the origin is p . Then p - ai is perpendicular to p ...
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Common terms and phrases
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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