IIT JEE , AIEEE Forum - Mathematics , Vectors

hit_ur_heart

Friends let me write the solution of this problem and also the mistake in the solution provided by rashmi

What rashmi has done is that she has taken 3 points and then she draws a plane passing through all those points and then taken 4th point and she says we will find a plane which is equidistant from the plane we have drawn and from the last point ...........................this is correct , but is it exhaustive ......................no definitely not
What about those cases in which plane will separate four points , two above it and two below it...................................definitely that case isnt covered , and there is
4C2/2 ways to do this(divided by two because planes will be same in half of the case) , i.e , 3 cases.
Total number of possible planes are 7

This is correct because it is exhaustive , means we cannot choose 4 points on same , plane as that will violate their non-coplanarity and 3,1 and 1,3 case are same , and (2,2) case is now covered.

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