190k views
2 votes
How many planes exist that go through exactly three vertices of a given cube?

Explanation: There are 6 planes that pass through exactly three vertices of a cube.
a. 1
b. 3
c. 6
d. 9

User Dlaliberte
by
8.2k points

1 Answer

2 votes

Final answer:

There are 6 planes that pass through exactly three vertices of a cube.

Step-by-step explanation:

To find the number of planes that go through exactly three vertices of a given cube, we can think about how many possible groups of three vertices we can form. In a cube, each vertex is connected to three adjacent vertices by an edge.

So, if we choose one vertex, we have 3 choices for the second vertex and 2 choices for the third vertex. However, each combination will result in the same plane. Therefore, we need to divide the total number of combinations by 6 (3! - the number of permutations of three vertices) to account for the duplications.

So, the total number of planes that go through exactly three vertices of a cube is 3! / 6 = 6.

User AlfaTeK
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories