how many planes can be formed from four non coplanar points taken three at a time?

Question

this ia a question related with 3-D and vectors.

Answer 1

3 non collinear points determine a plane. If you have 4 non coplaner points, you need to select 3 of these. This can be calculated by using combination. Hence 4C3 = (4 x 3 x 2) / (3 x 2 x 1) = 4. This problem is not related to vectors, as planes have no directions. A plane is a set of points on a flat surface extending in all directions. ( e.g. surface of a table expanding in all directions)

Answer 2

Coplanar Planes

Answer 3

4

Answer 4

3 points are always coplanar so from 4 non coplanar points, the number of planes formed
= C(4, 3)
= 4

Answer 5

this is question of combinations and permutations. Visualization helps but is not essential.

If there are 4 non-coplanar points say A, B,C, and D.

It takes 3 to make a plane.

Therefore:
ABC, ABD, ACD, BCD will make 4 unique planes given all points are non coplanar.

Notice that ABC, ACB, and CBA, etc are not listed because they are duplicates. This is why there is only 4, and not 24.

Answer 6

Geek has it right-4. While it does have to do with 3-d and vectors, the analysis uses neither. Simply define 4 points like EFGH and take them 3 at a time. You only have 4 combinations (order doesn't count).

Answer 7

The points are A, B, C, and C, and combinations of any three of them: A,B,C; A,B,D; A,C,D; and B,C,D these 4 planes can be obtained.

Answer 8

4 . It`s also a permutation of four taking three at a time.

Answer 9

If the points are A, B, C, and C, you can have four combinations of any three of them: A,B,C; A,B,D; A,C,D; and B,C,D.