If I have vectors $a = (1,0,0)$, $b = (0,1,0)$, and $c=(0,0,1)$ and I want to rotate them counterclockwise at rate $r$ rad/sec around vector (1,1,1). What are the formulas for $a, b, c$?
rotate vector around another vector
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1@SuperGuy If you want to rotate around some vector and not the origin, you should translate to the origin, do the rotation and retranslate. Try this reference, it gives a clear and full e$x$planation: Rotation About an Arbitrary Axis in 3 Dimensions, http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/ – 2011-09-23
2 Answers
Wiki Rotation matrix has a lot of information on rotating around X, Y, Z separately by $\alpha, \beta, \gamma$. These matrices can be multiplied together to get more complex rotations, but you will need to know how many rads to rotate around each axis.
And finally a rotation matrix that takes a vector and theta to create and can rotate a point/Vector around it. (I would like to know how this is Matrix is developed)
Rotation Matrix given Unit vector to rotate around and Theta
You will need to set up the rotation matrix $R$ and multiply $a' = Ra , b' = Rb , c' = Rc$. Use trial and error to figure +/- Theta to get clockwise rotation (This may depend on the "camera" orientation).
My own example on KA Shows a gray vector rotating around a red vector. Both are focused at the origin, so it creates a cone like shape.