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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 quaternion_rotation(quat, vector):
 """Apply the rotation represented by the quaternion to the vector Warning: This only works correctly for normalized quaternions. """

    dp = np.dot(quat[1:], vector)
    cos = (2*quat[0]*quat[0] - 1)
    return np.array([
        2 * (quat[0] * (quat[2] * vector[2] - quat[3] * vector[1]) + quat[1] * dp) + cos * vector[0],
        2 * (quat[0] * (quat[3] * vector[0] - quat[1] * vector[2]) + quat[2] * dp) + cos * vector[1],
        2 * (quat[0] * (quat[1] * vector[1] - quat[2] * vector[0]) + quat[3] * dp) + cos * vector[2]
    ], float)