Finding A and B to Satisfy A X B = B

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Homework Help Overview

The discussion revolves around the equation A X B = B, exploring the conditions under which this holds true. The subject area includes vector operations and properties, particularly focusing on the cross product in a three-dimensional context.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the implications of the cross product and its geometric interpretation. There are questions about the feasibility of the equation given constraints of the vectors A and B being in the x,y plane. Some participants are also considering how to approach the problem with three-dimensional vectors.

Discussion Status

The discussion is ongoing, with participants providing hints and prompting further exploration of vector properties. There is an emphasis on understanding the nature of vectors and the correct formulation of the cross product. Multiple interpretations of the problem are being explored without a clear consensus yet.

Contextual Notes

Participants are reminded of the importance of vector definitions and the correct mathematical expressions related to vector operations. There is an indication that the original poster may need to clarify their approach or assumptions regarding the dimensionality of the vectors involved.

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Homework Statement


Can A X B = B? If so, find A, and illustrate with a picture
B. If A=Axi+Ayj, find B such that A X B = Ayi-Axj


Homework Equations


I know A X B= ABsin\theta


The Attempt at a Solution

 
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You have missed the important part:

The Attempt at a Solution



Show some work, we won't simply give you the answers here!

I will give you one hint though. The expression you gave (AxB = ABsin..) is technically not correct.
The correct expression is:
\left| \vec{A} \times \vec{B} \right| = \left| \vec{A} \right| \left| \vec{B} \right| \sin \theta

In other words, it only gives you the length of the vector. Don't forget what a vector is!
 
Well i just need to know how to begin. I know If A is only in the x,y plane and B is only in the x,y plane then there's no way that's possible. However i don't know how to determine it with 3 different axis.
 
Nick89 said:
Don't forget what a vector is!

Student1, a vector is something with a magnitude and a direction.
 
If you have:
\vec{A} \times \vec{B} = \vec{C},
what do you know about the vector C in relation to A and B?
 

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