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Rotate point around line

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In addition, you need to make a correction step, since the axis of the axis/angle rotation is defined to pass through [0 0 0]. Hence, choose any point on the line, e.g. one of the both directly given points, as temporary origin. If p1 and p2 are the 2 given points, then a transformation like
T(p1) * R(p2-p1,alpha) * T(-p1)
is suitable, where T denotes a translation matrix and R the rotation matrix as suggested by Mike nl. (Notice please that I've used column vectors (e.g. OpenGL) in the formula above; reverse the order if you use row vectors (e.g. D3D) instead.)

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