Moving points of a line based on collision

Question

I have a line colliding with a sphere:

The grey spheres are the endpoints of the line.

The white sphere is colliding with the line.

The blue sphere is the point of collision.

What I want to do is essentially move the blue sphere (the point of collision) to the edge of the white sphere by moving the grey spheres (the line endpoints).

But, I want the grey spheres moved based on how close the colliding white sphere is.

e.g. in the image above, the white sphere is colliding roughly 80% to the right on the line. So the grey sphere on the left should have to perform 80% of the movement, with the left sphere doing 20%, resulting in the diagonal movement (shown below)

While a more central collision would result in equal movement from both:

Any advice on the maths required here?

What I have available in my equation is: The collision position The endpoint positions of the line The position and radius of the white sphere

I'd like to use this information to move the two endpoint positions.

Answer 1

So.. not as hard as I thought it would be:

        Vector3 d = (Vector3)lastCollisionPoint - sc;
        float dlen = d.magnitude;
        var movement = (sc + d * (r / dlen)) - (Vector3)lastCollisionPoint;

        t2.transform.position += Vector3.Lerp(Vector3.zero, movement, lerp);
        t1.transform.position += Vector3.Lerp(Vector3.zero, movement, 1f - lerp);

sc = sphere centre

lastCollisonPoint = the blue sphere collision point

t1 & t2 = the two points of the line