Arc between the start of 3D line and end of another 3D line (returned as a series of Vector 3 points) -- 3

We need the mathematics/code for the generation of an array of vector3 position points along an arc that goes from the end of one 3D line to the start of another 3D line. The arc is of arbitrary radius, but MUST extend from start/end of each respective line such that the centre of the arc is tangental to the direction axis of both lines. The arc must be circular, not an ellipse. The arc points should be evenly spaced between the line A end and line B start. The method following is the format that we wish the function to be completed. The code needs to be written in C#. List<Vector3> arcPoints(Vector3 lineAEnd, Vector3 lineBStart, Vector3 lineADirection, Vector3 lineBDirection, int arcPointCount) { //lineAEnd is the position of the end of incoming (1st) straight line //lineBStart is the position of the start of outgoing (2nd) straight line //lineADirection is the vector direction of the 1st line (IMPORTANT NOTE: the direction is pointing "towards" the arc). //lineBDirection is the vector direction of the 2nd line (IMPORTANT NOTE: the direction is pointing "away from" the arc). // arcPointCount is the number of point that want to be returned // the arcPoints method returns a generic list array of Vector3 position points that connects from the first line to the second through an ARC of arbitrary radius. The start and end of the arc need to be at the correspond ends line direction (i.e. origin of the arc is tangental line direction to both lineAEnd and lineBStart) } Please review the attached image for visual indication of the problem. NOTE that the lines and solution is required in THREE dimensions, the image is only for reference.