Question

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

Answer 1

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.