equidistant means of equal distance. so all point equidistant from (-4,2,1) and (2,-4,3) are those points which are of equal distance between (-4,2,1) and (2,-4,3). that is, if we call such a point (x,y,z), then at any time, the distance between (x,y,z) and (-4,2,1) is the same as the distance between (x,y,z) and (2,-4,3). that should give you a hint on how to solve the problem. use the distance formula. find the formula that gives the shortest distance between (x,y,z) and (-4,2,1) and then find the formula that gives the distance between (x,y,z) and (2,-4,3). then equate them and solve.