Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2019 / Paper 2 / 11 / a / iii / Solution

Writing $\overrightarrow{OA}=a\mathbf{e}+b\mathbf{f}+c\mathbf{g}$ and comparing Cartesian coordinates givesThe unique solution, guaranteed by the basis property, is $(a,b,c)=(-1,1,1)$. Thus