Question

Consider the set of eight vectors = {ai + bj + ck : a, b, c ∈ {−1, 1)}}. Three non-coplanar vectors can be chosen from V in 2^p ways. Then p is _____.

Answer 1

See Fig. The eight vectors are as shown in the following figure.

The total number of vectors is given by

⁸c₃ = 56

The total number of coplanar vectors is given by

2 x (6 x 2) = 24

That is

56 - 24 = 32 = 2⁵

Hence, p = 5.