Given the following two lines, prove that they are parallel, then find the distance between them...(adsbygoogle = window.adsbygoogle || []).push({});

(I have circled in red the two parts of the answer which I don't understand. Namely, why are they using the cross-product here, doesn't that give you a value perpendicular to the lines, hence a new vector that is on the parallel planes of the lines? The second part I highlighted I have no idea why they chose this.)

Could someone please explain the reasons to me? Something that I could visualize would be helpful.

Thanks, prior!

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# Using Cross-Product and Vectors to find the distance between parallel lines ?

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