How to rotate a Vec4 over Earth

Question

I am working with WorldWind Java. I want to rotate a Vec4 on x,y and z-axis on Earth's Sphere. I found a function calculating the north pointing tangent. My question is how can I rotate this vector. After rotation, I want to find the coordinates of the edge of the lines as shown on the pictures

https://drive.google.com/open?id=1NAWlP3GdipJ1TtrpRRBDKrF6DfrDMcxU

   public Vec4 computeNorthPointingTangentAtLocation(Angle latitude, Angle longitude)
    {
       // Latitude is treated clockwise as rotation about the X-axis. We flip the latitude value so that a positive
        // rotation produces a clockwise rotation (when facing the axis).
        latitude = latitude.multiply(-1.0);

        double cosLat = latitude.cos();
        double sinLat = latitude.sin();
        double cosLon = longitude.cos();
        double sinLon = longitude.sin();

        // The north-pointing tangent is derived by rotating the vector (0, 1, 0) about the Y-axis by longitude degrees,
        // then rotating it about the X-axis by -latitude degrees. This can be represented by a combining two rotation
        // matrices Rlat, and Rlon, then transforming the vector (0, 1, 0) by the combined transform:
        //
        // NorthTangent = (Rlon * Rlat) * (0, 1, 0)
        //
        // Since the input vector only has a Y coordinate, this computation can be simplified. The simplified
        // computation is shown here as NorthTangent = (x, y, z).
        //
        double x = sinLat * sinLon;
        double y = cosLat;
        double z = sinLat * cosLon;

        return new Vec4(x, y, z).normalize3();
    }