Adding vectors and applying rotation matrix using quaternion

Question

I have a problem and looking for help, see attached image. I have a number of points (x,y,z) which are treated as connected vectors (first point as first vector base, second point as first vector end AND second vector base, etc) and I need to know the minimal and maximal coordinate points of the whole connected structure. I only know that rotation matrix using quaternion should be applied in the process, but have no such experience. Any insights or links to similar example would be appreciated.

   auto rx = _coord_x.data(); auto ry = _coord_y.data(); auto rz = _coord_z.data();

// set up dimensions of coordinates

auto ncoords = number_of_vectors();


for (int32_t i = 0; i < ncoords; i++)
{
    //normalization
    float fact = 1.0f / std::sqrt(rx[i] * rx[i] + ry[i] * ry[i] + rz[i] * rz[i]);

    rx[i] *= fact; ry[i] *= fact; rz[i] = fact;

    // rotation matrix ??

  }

}