A vector problem

用戶36732

2012-09-21 11:31 pm

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

回答 (1)

天同

2012-09-22 12:43 am

✔ 最佳答案

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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