Left over from the big-bang beginning of the universe, tiny black holes might still wander through the universe. if one with a mass of 3 × 10^11 kg (and a radius of only 1 × 10^-16 m) reached earth, at what distance from your head would its gravitational pull on you match that of earth's? assume free-fall acceleration ag=9.83 m/s2.

The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].