How to calculate the rotation matrix in 3D in terms of an arbitrary axis of rotation? Given a unit vector $V=V_{x}e_{x}+V_{y}e_{y}+V_{z}e_{z}$ How to calculate the rotation matrix about that axis?
Rotation matrix in terms of axis of rotation
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linear-algebra
matrices
rotations
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1See e.g. [Wikipedia](http://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle) – 2012-12-09
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0But the Wikipedia page just tells the formula . I want to know how to derive this – 2012-12-09
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3It's just a conjugation of the simple matrix for a rotation around the $z$-axis, which is effectively just 2 x 2 matrix, by another rotational matrix that rotates the North pole to the point $V$, which is a product of rotation in the theta-direction and the phi-direction to get where you need to get. Conjugation by $U$ is $URU^{-1}$ where the product is matrix product. It's possible ineffective to write these things without matrices so if you don't know matrices, this is a reason to learn them. At any rate, it's not really physics, it's linear algebra and geometry and a basic one. – 2012-12-09
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0thanks a lot. It's pretty simple . I think it can also be solved by considering an arbitrary vector ,taking the projection of that vector into the plane perpendicular to the axis of rotation and rotate that vector . – 2012-12-09
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0This is a math question and belongs on [math.se] – 2012-12-09