under what conditions three vectors give a zero resultant?
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vectors are in the form of equilateral trangle
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I'm going to assume that what you mean by 'orientation of a vector' is the set of direction cosines of the vector. What I mean is that, for a vector v= (a1 a2 ... an)^T, the direction cosines are a1/|v|, a2/|v|, ... an/|v|.
Any three vectors that cancel each other sum up to zero. So any three vectors v1,v2,v3 satisfying v1+v2+v3=0 will do. Their direction cosines, however, are rather arbitrary. Essentially, two of the vectors can have any arbitrary directions, while the third must satisfy v3=-v1-v2. So the answer to this question is"any directions whatsoever".
Any three vectors that cancel each other sum up to zero. So any three vectors v1,v2,v3 satisfying v1+v2+v3=0 will do. Their direction cosines, however, are rather arbitrary. Essentially, two of the vectors can have any arbitrary directions, while the third must satisfy v3=-v1-v2. So the answer to this question is"any directions whatsoever".
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