A,B,C,D are four distinct points in space no, three are collinear and theyare not coplanar. The n.o of planes that are there in space ,each of which is equidistant from A, B,C,D

1)5 2)7 : 3)8 4)12

Dear Student
There are two cases 1) Three points on one side of plane and one point on the other side
2) Two points on one side and two on other. In case 1) there are 4 possibilities because the one point can be anyone one of the 4 points . In case 2) There are three cases since two points can be selected out of 4 in 4C2 /2 . It is divided by two to A,B,C,D are four distinct points in space no, three are collinear and theyare not coplanar. The n.o of planes that are there in space ,each of which is equidistant from A, B,C,Dnot allow repetitions . So total 4+3=7 ways . Good question . Hope you got it