標題:
A vector problem
發問:
http://upload.lsforum.net/users/public/m11264vectorr248.png Four vectors (A,B,C,D) all have the same magnitude. The angle between adjacent vectors is 45 as shown. The correct vector equation is: 1. A-B-C+D = 0 2. B+D-√(2)C = 0 3. A+B = B+D 4. A+B+C+D = 0 5. (A+C) / √2 = -B
最佳解答:
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This question doesn't invlove any physics principles. It is only a matter of mathematics. From the given diagram, the four vectors A, B, C, D can be written as, A = Fj B = Fcos(45)i + F.cos(45)j C = Fi D = F.cos(45)i - F.cos(45)j where F is the magnitude of each vector, and i and j are unit vectors in the x and y directions respectively Thus, it can be easily shown that option (2) is correct. B + D = [ Fcos(45)i + F.cos(45)j] + [ F.cos(45)i - F.cos(45)j] = 2F.cos(45)i = (√2)Fi hence, B + D - √2C = (√2)Fi - (√2)Fi = 0
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