Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 2 / 1 / b / Solution

Equating vector components givesThe third component first forces $\gamma =0$, then the second forces $\beta =0$, and the first gives $\alpha =0$. ThusEquivalently, the nonzero scalar triple product proves that these three vectors are linearly independent.