If we have two nonzero vectors in 3-space [itex]\vec{V_1}=a_1\vec{i}+b_1\vec{j}+c_1\vec{k}[/itex] and [itex]\vec{V_2}=a_2\vec{i}+b_2\vec{j}+c_2\vec{k}[/itex], define [itex]\vec{V^'_1}=a^2_1\vec{i}+b^2_1\vec{j}+c^2_1\vec{k}[/itex] and [itex]\vec{V^'_2}=a^2_2\vec{i}+b^2_2\vec{j}+c^2_2\vec{k}[/itex]. How can we prove that if [itex]\vec{V_1}-\vec{V^'_1}[/itex] is parallel to [itex]\vec{V_2}-\vec{V^'_2}[/itex], then [itex]\vec{V_1}[/itex] is parallel to [itex]\vec{V_2}[/itex]?(adsbygoogle = window.adsbygoogle || []).push({});

Any ideas? I've been thinking about this for a while and it's bugging me because I think it should be true but I can't figure out how to prove it.

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# Help with a proof

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