Question

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

Answer 1

V = ai + bj + ck : a, b, c ∈ {-1, 1}

Total number of selection  = ⁸C₃

No. of coplanar vectors = 6 x 4 = 24 

Total number of non co-planar vet 

- ⁸c₃ - 24 = 32 = 2^p 

= P = 5