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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def pix2sky_vec(self, pixel, r, theta):
 """ Given and input position and vector in pixel coordinates, calculate the equivalent position and vector in sky coordinates. Parameters pixel : (int,int) origin of vector in pixel coordinates r : float magnitude of vector in pixels theta : float angle of vector in degrees Returns ------- ra, dec : float The (ra, dec) of the origin point (degrees). r, pa : float The magnitude and position angle of the vector (degrees). """

        ra1, dec1 = self.pix2sky(pixel)
        x, y = pixel
        a = [x + r * np.cos(np.radians(theta)),
             y + r * np.sin(np.radians(theta))]
        locations = self.pix2sky(a)
        ra2, dec2 = locations
        a = gcd(ra1, dec1, ra2, dec2)
        pa = bear(ra1, dec1, ra2, dec2)
        return ra1, dec1, a, pa