# Angle between two vectors in 3d

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developer 2011년 9월 20일
댓글: Bruno Luong 2023년 2월 1일
Hello,
I have two vectors in 3d and i want to find the angle between those two vectors.

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### 채택된 답변

Jan 2011년 9월 20일
Or:
angle = atan2(norm(cross(a,b)), dot(a,b))
See this compact discussion about this topic: CSSM: Angle between two vectors . Only 71 replies (Google finds 89 replies, so I assume 18 spam messages?) and 68300 views currently...
[EDITED]: W. Kahan suggested in his paper "Mindeless.pdf":
2 * atan(norm(x*norm(y) - norm(x)*y) / norm(x * norm(y) + norm(x) * y))
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Bruno Luong 2023년 2월 1일

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### 추가 답변(3개)

Lucas García 2011년 9월 20일
You can use the subspace function to find the angle between two subspaces:
>> subspace([1;0;0],[0;1;0])
ans =
1.5708
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I have 3 points in a line( suppose) and one calculations point separately. A(1,1,1)B(2,2,2)C(3 3 3) in a line and P( 5 5 5) as separate. I want to calculate angle A which is subtended by distance AP. And similar for BP,CP. Is it possible to find angles or make program to calculate these angles at once?

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David Young 2011년 9월 20일
acos(dot(v1, v2) / (norm(v1) * norm(v2)))
EDIT: Having seen Jan Simon's reply, and the long thread at CSSM that he refers to, I realise that the formula I proposed is not a particularly good one. The two methods in Jan's reply are both likely to be preferable.
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Jan 2011년 9월 20일
Mathematically identical, but numerically more stable, when the vectors have very different lengths:
acos(dot(v1 / norm(v1), v2 / norm(v2)))

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rashi 2018년 6월 15일
hi I want to find the angle in azimuth and elevation plane between wo vectors in 3d. please help

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