Calculating an angle from vectors
Author
Hi there guys,
Sorted
Thanks for your help guys.
Neil
[Edited by - neilski_2003 on April 25, 2006 6:22:36 AM]
The dot product of two vectors is the cosine of the angle between them times the magnitudes of the vectors. So, if you have two vectors A <x, y> and B <z, w> with an angle T between them, then:
dot(A, B) = cos(T)*mag(A)*mag(B)
so
T = arccos(dot(A,B)/(mag(A)*mag(B))
with
dot(A,B) = x*z + y*w
mag(A) = sqrt(x*x + y*y)
mag(B) = sqrt(z*z + w*w)
dot(A, B) = cos(T)*mag(A)*mag(B)
so
T = arccos(dot(A,B)/(mag(A)*mag(B))
with
dot(A,B) = x*z + y*w
mag(A) = sqrt(x*x + y*y)
mag(B) = sqrt(z*z + w*w)
I might not entirely understand what you're asking for. If I don't, then I apologize.
To find the angle between two vectors A and B, use the geometric formula for the dot product:
A dot B = |A| * |B| * cos(alpha)
where alpha is the angle in question. With some manipulations, we have:
cos(alpha) = (A dot B) / (|A| * |B|)
alpha = cos-1((A dot B) / (|A| * |B|))
To find the angle between two vectors A and B, use the geometric formula for the dot product:
A dot B = |A| * |B| * cos(alpha)
where alpha is the angle in question. With some manipulations, we have:
cos(alpha) = (A dot B) / (|A| * |B|)
alpha = cos-1((A dot B) / (|A| * |B|))
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