Possible Error in "distance between planes " video on linear algebra.

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kaibarreraera

9 de janeiro de 2021 11:18

At 6:27 sal is calculating a cross product of two vectors in 3d space. He calculates i as (a2×b3)-(a3×b2) which is fine. What I'm confused about is why he calculates j as (a1×b3)-(a3×b1) instead of (a3×b1)-(a1×b3) ? I specifically remember him saying that calculating j goes against your normal intuition to cross multiply the same way you would for i and k. I would post this on the video but I don't have enough points to comment and need an answer quickly.

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Evan Lewis

9 de janeiro de 2021 19:48
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Hi kaibarreraera,

If you break the j component up into a smaller matrix, you get the following:

| 2 1 | = (2)(1) - (4)(1) = -2
| 4 1 |

The j component of the cross product is always the negative value of the smaller matrix determinant, so the final result is -(-2) = +2.

I hope this helps! Please let me know if you have any additional questions!
kaibarreraera

10 de janeiro de 2021 02:19
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I think I understand now. Perhaps in the previous video he was strictly adding each determinant meaning the j component would have to be (4)(1) - (2)(1) = +2 to correct for the sign. However if we are following the structure of +i -j +k instead of +i +j +k like the above, we would have to use (2)(1) - (4)(1). Thank you!

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Possible Error in "distance between planes " video on linear algebra.

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