What is the Result of i X i in a Cross Product?

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Homework Help Overview

The discussion revolves around the properties of the cross product in vector mathematics, specifically focusing on the result of the cross product involving the unit vector i and its implications for vector B in a given context.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the implications of the cross product i X j resulting in k and question the components of vector B. There are discussions about the necessity of specific components in B to achieve the desired result in the cross product.

Discussion Status

The conversation is ongoing, with participants providing mathematical reasoning and questioning assumptions about the components of vector B. Some participants assert that B must have a specific direction, while others challenge these assertions, indicating a lack of consensus on the interpretation of the results.

Contextual Notes

There is a focus on the constraints of the problem, particularly regarding the components of vector B and the implications of the cross product. Participants are examining the mathematical relationships without reaching a definitive conclusion.

krot
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in the end of this
http://i29.tinypic.com/5fktjo.jpg

i got to the point where it asks what B is
i think that because i X J = K then b should be in the direction of J

but they have a different conclusion
why??
 
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All you can conclude is that B has a j component.
 
its only in j direction
it can't have a component of other vector
because in order to transform i to k
we need pure j
 
krot said:
its only in j direction
it can't have a component of other vector
because in order to transform i to k
we need pure j
No. Let B = ai + bj + ck. When you take the cross product, each term must give a k-component or 0. We know that c must equal 0, since i X k = -j. But what about a?
 
one vector is(1,0,0)
the result vector is (0,0,1)
i do this determinant to find the cross product
|i j k |
|1 0 0|
|x y z|
it gives us i*0 +j*z +k*-y or (0,z,-y)
but our result vector is (0,0,1)
so z=0 and y=-1

y=-1 is -j vector

there is no a here
i showed purely by math that the result is pure -j vector

there is no way to have components from other vectors
 
krot said:
i showed purely by math that the result is pure -j vector
No you didn't. What's i X i?
 

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