 | Duncan Farquharson Gregory - 1845 - 364 pàgines
...(41) To find the angle between two planes, of which the equations are Ax + By + Cz = D, A'x + By + C'z = D. The angle between two planes is the same...A', B, C', we have, if 0 be the angle between them, a AA' + BB" + CC' COS V = , which expression therefore determines the angle between the two planes.... | |
 | Duncan Farquharson Gregory - 1852 - 352 pàgines
...41. To ßnd the angle between two planesj of which the equations are. Ax + By + Cz = />, Ax + By + C'z = D'. The angle between two planes is the same...direction-cosines of the normals being proportional to A, B, (7, A, /?', C", we have, if в be the angle between them, AA' + BB' + CС' """ " * (A* + B* + C*)*... | |
 | James White - 1878 - 160 pàgines
...p cosy" ABC' .__. -- , or -=- = , ' where A, B, and C are proportional to cos a, cos ft, and cos y. The angle between two planes is the same as the angle between their normals, consequently (Art. 152) the condition that two planes Ax + By + Cz = D and A'x + B'y... | |
 | Edward Albert Bowser - 1880 - 314 pàgines
...Let Ax + By + Cz + D = 0, (1) and A'x + B'y + C'z + D' = 0, (2) be the equations of the two planes. The angle between two planes is the same as the angle between two lines drawn perpendicular to them. If the equations of these two perpendiculars are x — az + a, y = bz + |3 ; ... and x = a'z + «',... | |
 | 392 pàgines
...see that cos 6 = cos a cos a' + cos ft cos ft' + cos y cos y'. T. <feN. 17 Angle between Two Planes. The angle between two planes is the same as the angle between the normals to the planes. If the planes are given in the ' normal form ' the direction cosines of... | |
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The angle between two planes is the same as the angle between two lines drawn perpendicular to them ; that is, it is equal to the angle between their normals. 