\begin{array}{l}
\lambda(a,b,c)=(\lambda a,\lambda b,\lambda c),
\vspace{0.5em}\\
(a_1,b_1,c_1)\pm(a_2,b_2,c_2)=(a_1\pm a_2,b_1\pm b_2,c_1\pm c_2),
\vspace{0.5em}\\
(a_1,b_1,c_1)(a_2,b_2,c_2)=a_1a_2+b_1b_2+c_1c_2,
\vspace{0.5em}\\
(a,b,c)^2=(a,b,c)(a,b,c)=a^2+b^2+c^2
\end{array}