...acute or obtuse. 28. To find the angle between two planes Ax + By + Cz + D = 0, A'x + B'y + C'z + D' = 0. The angle between the planes is the same as the...and thence, Arts. 13, 14, we have AA' + BB' + CC' *! "Tf^F+F+T^p8 sin"^=^R ~ (A* + B* + C*) (A"' + B" + C") Hence the condition that the planes should...

..." D cular is + Jf + C* 24. The angle between any two planes whose equa. tions are Ax + By + Cz = D, is the same as the angle between the perpendiculars on them from the origin. But the direction-cosines of these perpendiculars are (Art. 23) ABC ** JA'+B*+C** A' B' C' and the...

...lune is the angle that the planes of the great circles make with each other. As we have seen (§ 116), the angle between the planes is the same as the angle between the semicircles at their intersection, and that is measured by the arc of a great circle included between...