If there are vectors V, A, B, and C starting from a common point O but no coordinate system is given.

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I know to find the angle between two vector, we could use a dot product between the vectors. For example, the angle between vector V and A will be $\arccos(V\cdot A)/(|V|*|A|)$, similar idea to find the angle between vector V and B, vector V and C.

Since the order of vector in the dot product does not matter, so the angle between V,B and the anvle between V, C are same. My question is, if I used vector v as a reference always, and I would like the angle defined counter-clockwise such that the angle between V, B is 160 degree and the angle between V, C is 200 degee. Anyway to find the angle between two vector defined in that way? Thanks.


1 Answer 1


Suppose that we have just two intersecting vectors. Then, we shall both agree that we are going to have 4 angles –but actually just two different angles– 2 obtuse angles and 2 accute ones.

If you claim to have at least the length of those very same vectors, we can actually lengthen them in the opposite direction as advantageously as it might be, for us, in that case.

At least I reckon –if I am not mistaken– two different ways of solving this problem. One involves isosceles triangles and, the other one right triangles.

By an induction reasoning, you should be able to use the very same techniques for an unlimited number of intersecting vectors.


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