Current Events > Any of ya'll good at linear algebra?

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This is probably pretty simple but I'm dumb, how do I calculate a cross product u x v if both u and v are given as cross products? Do I have to convert them back to vectors? Because I have no idea how to do that

@Eevee-Trainer
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You mind letting me see the problem @MordecaiRocks ? Not going to guarantee I have a solution but it's worth a shot because I *think* I have an idea of what you're getting at.
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do your own fucking homework
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I can draw a line if that's what you mean.

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Linear algebra? Are you in 8th grade? lmao
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Eevee-Trainer posted...

You mind letting me see the problem @MordecaiRocks ? Not going to guarantee I have a solution but it's worth a shot because I *think* I have an idea of what you're getting at.

@Eevee-Trainer

The problem is

"Let u = 4i x 5j and v = j x k. Compute u x v and v x u"

REMercsChamp posted...

do your own fucking homework

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I assume the i, j, and k have a little carat above their heads denoting the fact that they're unit vectors?

If so, remember that:

* i-hat is the vector [1, 0, 0]
* j-hat is the vector [0, 1, 0]
* k-hat is the vector [0, 0, 1]

Applying the scalar rule should get you 4i and 5j, and then you can find their cross product the normal way to find u. Similarly, find the cross product for v by the cross product of j-hat and k-hat. Then you can find u x v and v x u (though you'll want to note the property v x u = -(u x v) to save some time).

Seems an unusually roundabout way to go about it though, thought for a second there might have been a typo in the thing.

If you need help finding the cross product I can help with that too, though just know it's going to be the whole "find the determinant of a 3x3 matrix" way.
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Eevee, math major?
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Scotty_Rogers posted...

Linear algebra? Are you in 8th grade? lmao

Um, what?
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DoGCyN posted...

Eevee, math major?

Yup. Though linear algebra is a bit of a weak point and I don't think I've done cross products since like ... physics tbh.

Kinda got them hammered into my head there though.
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@MordecaiRocks

https://www.physicsforums.com/

They're going to be happy to help you. And probably better than most people here, too.
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Find u and v separately, then cross product again

u = 20k
v = i

u x v = 20j
v x u = -20j

Just remember that
i x j = - j x i = k
j x k = - k x j = i
k x i = - i x k = j
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awesome999 posted...

Just remember that
i x j = - j x I = k
j x k = - k x j = i
k x i = - i x k = j

*facepalm* I forgot about that being a thing. I just calculated it manually.
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(A x B) x (C x D) = det(A,B,D) * C - det(A,B,C) * D
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The cross product of two vectors is itself a vector. The cross product of two cross products is just another vector.
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@frozenshock
@Eevee-Trainer
@awesome999

Thanks guys, appreciate it! Figured it wasn't as complicated as it seemed

No problem, anything else?
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awesome999 posted...

No problem, anything else?

I'm good for now but I'm sure I'll get stuck on something again in the future lol