hello every one.

I am trying to make a collision response in 3D, and that includes rotation. I know that rotation is a vector quantity, but I don't know how to use such a vector.
if the vector is [2,6,7], should I rotate the object 2 radians around the X-axis, 6 radians around the Y-axis, and 7 radians around the Z-axis?

Rotations are usually matrices, not vectors. I don't know where you got that vector, but it is probably a non-normalized representation of the axis of rotation.

This Wolfram page may be helpful: http://mathworld.wol...tionMatrix.html.

I mean angular velocity, see http://en.wikipedia.org/wiki/Angular_velocity.

Ah. In that case, you treat the center of mass as a particle in 3D space. To quote Wikipedia's Particle in three dimensions subsection:

"The angular velocity in this case is generally thought of as a vector, or more precisely, a pseudovector. It now has not only a magnitude, but a direction as well. The magnitude is the angular speed, and the direction describes the axis of rotation."

in the case of [2,6,7]

sqrt(2^2+6^2+7^2) = 9.43 radians per second, which is very close to 3 rotations per second.

[2,6,7]/9.43 = [0.21, 0.63, 0.74]

So the object is doing about 3 rotations per second clockwise on the [0.21, 0.63, 0.74] axis.

edit: I forgot to comment on the direction of rotation.
The rotation is always clockwise. To get a counter-clockwise rotation about a given axis, make a rotation about the negative of that axis.
For example, 3 counterclockwise rotations per second about the [0.21, 0.63, 0.74] axis would be expressed as [-2,-6,-7].

now i get it, thanks