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\[ \vec{u} = (x_{1}, y_{1}, z_{1}) \vec{v} = (x_{2}, y_{2}, z_{2}) \vec{u} = \vec{v} \iff x_{1} = x_{2} \land y_{1} = y_{2} \land z_{1} = z_{2} \]
\[ \vec{u} = (x_{1}, y_{1}, z_{1}) \vec{v} = (x_{2}, y_{2}, z_{2}) \vec{u} = \vec{v} \iff x_{1} = x_{2} \land y_{1} = y_{2} \land z_{1} = z_{2} \]