Consider the set of eight vectors $\left\{a\widehat{i}+b\widehat{j}+c\widehat{k}:a,b,c\in \{-1,1\}\right\}$. Three non – coplanar vectors can be choosen from V in $2^P$ ways. Then P is…….

Given 8 vectors are (1,1,1),(-1,-1,-1),(-1,1,1),(1,-1,-1),(1,-1,1),(-1,1,-1),(1,1,-1),(-1,-1,1)

We select three group of diagonals and its opposite $4_{C_3}$

Then one vector from each group can be selected in 2x2x2 ways

Total number of ways =32=$2^5,p=5$