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chrisplusian
 one year ago
Have a question about the angle related to cross product and dot product as it relates to to the unknown angle between two vectors.
chrisplusian
 one year ago
Have a question about the angle related to cross product and dot product as it relates to to the unknown angle between two vectors.

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chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0When a question asks you to find "the minimum angle between" two vectors, is it ok to use the dot product definition? Or do you have to use cross product to find the "minimum' angle?

phi
 one year ago
Best ResponseYou've already chosen the best response.0dot product is ok. they are just saying they want angle x in dw:1442182565780:dw

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0The question literally says Given vectors A and B determine the minimum angle between A and B

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0So i did it with the dot product and got the larger of the two angles, and AI was wondering if I had to use the cross product to ensure I get the smaller of the two? It has been about two years since I have done any three dimension vector operations and my mind is fuzzy when it comes to the topic

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0post or link the question,

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0So the question gives specific values for A and B I am just asking about the concept

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0Ok substitute A =3i + j 2K, an B = 2i  5j + k into the above question and that is what it says verbatim

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0But I am not looking for help with this specific question, I am trying to find out the concept in general, because my textbook says that to find the "minimum" angle you use cross product. That seemed sketchy to me so I wanted to inquire about the concept

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0these are 2 planes, and they are defined by their normals. the angles between those normals are fixed. you can cross them or dot them or whatever, just remember the right hand rule.

phi
 one year ago
Best ResponseYou've already chosen the best response.0I think the are saying dw:1442183770146:dw if you use dot product and get an angle bigger than 90º, do 180x to find the "minimum angle"

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0**my textbook says that to find the "minimum" angle you use cross product** nonsense

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0@IrishBoy123 that was my question.... is that nonsense?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0work your question for this: A =3i + j 2K, B = 2i  5j + k your suggestion!

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0the cross product of A & B will give you a third vector that is at right angles to both of these according to the definition \(A \times B = AB\sin\theta \ \hat n\). importantly, the magnitude of that vector will equal \(AB\sin\theta\) where \(\theta \) is the angle between the vectors. so \(sin \theta = \frac{A \times B}{A \ B}{}\) so you can do it that way, find the cross product (which will be a vector), then plug its *magnitude* into the equation the dot product on the other hand will give you just a number which equals the projection of either vector onto the other. and it's simpler, chorewise again we have the definition \(A \bullet B = AB \cos \theta \) so \(cos \theta = \frac{A \bullet B}{A \ B}{}\) you may then run into the problem as indicated above dw:1442224407955:dw i did when i cranked out the numbers that's a bit of a mouthful so i hope it is helpful :p
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