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For most combatants, age old nationist philosophies determined the course of the war. For centuries, the German people have felt that their national destiny, their greatest chance for security, lay in domination of the east, ie, European Russia/Ukraine. German settlers were scattered throughout the region and were very influential. Otherwise Germany had little interest in expansion. The battles in France, Norway, etal. were really defensive in nature, where Germany tried to gain an edge before the western Allies grew too strong. Thus the question, why did the western Allies fight? Their centuries old goal had been to limit German power. Despite having vast overseas empires and large European territories, both England and France considered any German move, no matters how localized or trivial, a mortal threat to their national security. This feeling led them to put all their military involvement into anti-German efforts. Eventually this tension had to break, as it did in both world wars. Russian historical aims have long been consistent also, regardless of the regime in power. Russia has lusted for warm water ports on the Baltic, Black, and Mediterranean seas. Longer term positions have been to expand that position to the Persian Gulf or perhaps the Indian ocean. Like Britain and France, Russia had a vast empire where minority peoples were ruthlessly controlled by any means necessary. The desire of the Russians to press west and south put them on a collision with German speaking peoples in Germany and the Balkans, leading to those nations fighting in both world wars. Japan, being a small island nation with few Natural Resources, desired national security too. They sought to gain this by control of surrounding territories such as Korea, Phillipines, north China, and southeast Asia. Being isolated for centuries prior to 1870, these goals were fairly recent in the national philosophy, contrasted with the various European goals which had been around for centuries. They were thus rather easily discarded by the populace following the defeat of 1945. The USA had no real goal in the war, thus their reluctance to join in early. The USA, alone among these major powers, was fairly insulated from invasion but at the same time in possession of huge natural resources. The USA thus had only a limited oversease empire, had not come into conflict with any overseas power other than Japan, and had no need to expand territorially. In many ways, Germany and the USA were similar in their national goals, except that the USA had reached hers by 1900. Germany desired to have a similar position with limited overseas empire and a fairly large geographical territory with defensible borders, just like the USA. At wars end Japan and Germany were defeated. Germany's goal of national security was shattered, perhaps for all time. Japan lost all their empire but was (and is) under the military shelter of the USA and has thus lost most of their militaristic zeal. Russia achieved most of her goals by shattering German power in the east and southeast of Europe and replacing it with her own. Further Russian expansion into the Middle East and India was largely blocked by NATO. Britain and France, with the most short sighted views on world history of the major combatants, 'won' their game by crushing German power. And what did they reap? Both were exhausted by the effort and had to relinquish empires gathered by their ancestors over centuries of blood, sweat and toil. Both were faced with a much more ruthless and dangerous enemy than Germany, in a nuclear armed Soviet Russia - now with outposts only 150 miles east of the Rhine. The efforts expended by these two has placed them in long term decline as world powers until, at present they represent scarcely credible 'regional' powers with further declines likely in the future. The USA, which entered the war with almost no real nationist goal, came out with a world view based on free trade for all and containment of aggressive Soviet expansion. To a large extent, those goals by the USA have been met in the year 2006 with economic capitalism the dominant world system and communism virtually dead.

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Q: What were the Allies' and Axis's political policies and philosophies?
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If i have a points a and b in 3d space and i want to move b n units closer to a how do i determine how much to change b's x y and z values?

How to move a specific distance along a line determined by 2 points in 3d space! Specific distance = m Distance between the 2 points = D Distance to move along line from Point #2 toward Point #1 = Displacement = m Determine the coordinates of the point M (c, d, e), which is m units closer to Point#2 Given 2 points Point #1 (a, b, c) Point #2 (g. h, i) 1. Find the distance between the 2 points using Pythagorean Theorem Think of moving from Point #1 to Point #2 by moving along the x-axis, then the y-axis, then the z-axis. (g-a) = distance moved along the x-axis (h-b) = distance moved along the y-axis (i-c) = distance moved along the x-axisS D = [(g-a)^2 + (h-e)^2 + (i-c)^2]^0.5 2. Determine the coordinates of the unit vector by dividing the distance moved along each axis by D. Coordinates of unit vector = [(g-a) ÷ D], [(h-b) ÷ D], [(i-c) ÷ D] x coordinate of unit vector = (g-a) ÷ D y coordinate of unit vector = (h-b) ÷ D z coordinate of unit vector = (i-c) ÷ D Unit vector = [((g-a) ÷ D)^2 + ((h-e) ÷ D) ^2) + ((i-c) ÷ D) ^2]^0.5) = 1 If the value of the unit vector does not =1, go back and check your work. 3. Multiply each coordinate of the unit vector by m to determine the coordinates of the vector m. These coordinates will be added to coordinates of Point #1 to determine the coordinates of Point #3. x coordinate of m vector = m * (g-a) ÷ D y coordinate of m vector = m * (h-b) ÷ D z coordinate of m vector = m * (i-c) ÷ D 4. To determine the coordinates of Point #3(d, e, f) that is m cm from Point #1 toward Point #2, add the coordinates of the m vector to the coordinates of Point #1. d = x coordinate of Point #3 = a + (m * (g-a) ÷ D) e = y coordinate of Point #3 = b + (m * (h-b) ÷ D) f = z coordinate of Point #3 = c + (m * (i-c) ÷ D) 5. To determine the distance from Point #1 (a, b, c) to Point #3 (d, e, f), use Pythagorean Theorem D = [(d-a)^2 + (e-b)^2 + (f-c)^2]^0.5 The answer should be m. I wanted to move 2 cm from Point #1 toward Point #2, and I did. Now let's see if this method works!! Point #1 = (2,3,1), Point #2 = (6,9,3) I want to move 2 cm from Point #1 toward Point #2, that means m = 2 cm. 1. Find the distance between the 2 points using Pythagorean Theorem D = [(g-a)^2 + (h-e)^2 + (i-c)^2]^0.5 D = [(6-2)^2 + (9-3)^2 + (3-1)^2]^0.5 D = [(4)^2 + (6)^2 + (2)^2]^0.5 D = [16 + 36 + (4)]^0.5 D = 56^0.5 D = 7.4833 So the line between these Point #1 and Point #2 is 7.483 units long 2. Determine the coordinates of the unit vector by dividing the distance moved along each axis by D. Distance moved along x-axis = 4 Distance moved along y-axis = 6 Distance moved along z-axis = 2 x-coordinate of unit vector = 4 ÷ 7.4833 = 0.5345 y-coordinate of unit vector = 6 ÷ 7.483 = 0.8018 z-coordinate of unit vector = 2 ÷ 7.483 = 0.2673 Length of unit vector = [(0.5345)^2 + (0.8018)^2+ (0.2673)^2]^0.5 = 1 The length of the unit vector should = 1 3. Multiply each coordinate of the unit vector by m to determine the coordinates of the vector m. x coordinate of m vector = m * (g-a) ÷ D = 2 * 0.5345 = 1.069 y coordinate of m vector = m * (h-b) ÷ D = 2 * 0.8018 = 1.6036 z coordinate of m vector = m * (i-c) ÷ D = 2 * 0.2673 = 0.5346 m vector = [1.069^2 + (1.6036)^2 + (1.5346)^2]^0.5 = 2 4. To determine the coordinates of the Point #3 (d, e, f) that is m cm from Point #1 toward Point #2, add the coordinates of the m vector to the coordinates of Point #1 (a, b, c). Point #1 = (2, 3, 1) x coordinate of Point #3 = 2 + 1.069 = 3.069 y coordinate of Point #3 = 3 +1.6036 = 4.6036 z coordinate of Point #3 = 1+ 0.5346 = 1.5346 Point #3 = (3.069, 4.6036, 1.5346) 5. To determine the distance from Point#1 to Point #3, use Pythagorean Theorem D = [(d-a)^2 + (e-b)^2 + (f-c)^2]^0.5 D = [(3.069-2)^2 + (4.6036-3)^2 + (1.5346-1)^2]^0.5 D = [(1.069)^2 + (1.6036)^2 + (0.5346)^2]^0.5 = 2 D = 2 cm I wanted to move 2 cm from Point #1 toward Point #2, and I did.