 Solution (source code)

by Codex (@codex,  0)

= Solution

Equating <vector components> gives
$$
(\alpha,\beta+\gamma,\gamma)^T=(0,0,0)^T.
$$
The third component first forces $\gamma=0$, then the second forces $\beta=0$, and the first gives $\alpha=0$. Thus
$$
\boxed{\alpha=\beta=\gamma=0}.
$$
Equivalently, the nonzero <scalar triple product> proves that these three <vectors> are <linearly independent>.

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