What Is the Cross Product of Two Vectors?

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This is an almost impossible question to answer without knowing what would qualify as a satisfactory answer. I dip my toes into Lee algebra in my particle physics course, and it feels like the answer is hidden there. For those of you who don't know, if I have two vectors, the two vectors in three-dimensional space always describe a plane. You can always imagine the plane in which both vectors are simultaneously embedded. So the cross product of those two vectors is a third vector that is perpendicular to that plane.

Welcome to the February 2023 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreons, whittle them down to a more manageable number — based primarily on whether I have anything interesting to say about them, not whether the questions themselves are good — and sometimes group them together if they are about a similar topic. Enjoy!

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The big news this month is the successful awarding of the first ever Mindscape Big Picture Scholarship. Congratulations to Lyat Melese and Rehman Hassan! We continue to collection donations for next year’s scholarship contest.

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