Vector Cross Product Homework: Find 3rd Vector Perpendicular to C & D

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Homework Help Overview

The problem involves finding a third vector that is perpendicular to two given vectors, C and D, which are defined in terms of other vectors A and B. The context is within vector algebra, specifically focusing on the cross product and properties of orthogonal vectors.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the method of finding the cross product of vectors C and D. There are attempts to manipulate the expressions for C and D, and some participants question the validity of their algebraic manipulations and the assumptions behind the operations.

Discussion Status

The discussion is active, with participants sharing their attempts at the cross product and clarifying the steps involved. Some guidance has been provided regarding the properties of cross products, but there is no explicit consensus on the final form of the answer.

Contextual Notes

There is a mention of the absence of unit components for the vectors, which adds a layer of complexity to the problem. Participants are navigating the constraints of the problem setup and the rules of vector operations.

xcgirl
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Homework Statement



C= B|A| + A|B|
D= A|B|-B|A|
C and D are orthogonal
Find a third vector perpendicular to both C and D

Homework Equations



[AxB] = |A||B|sin(theta)

The Attempt at a Solution



I know that to find the answer I need to find the cross product of C and D. I have done similar problems, but the unit components (i,j,k) have always been given. I can't figure out a way to do this without having those.
Thanks for any help, even a hint!
 
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CXD = (B|A| + A|B|)X( A|B|-B|A|)
Do the cross multiplication of right hand side. Note that AXA = BXB = 0 And AXB = -BXA
You can multiply the magnitudes of A and B directly.
 
so I can do...

BxA|A||B| + BxB|A||A| + AxA|B||B| - AxB|B||A|
BxA|A||B| - AxB|B||A|

so would that be the final answer? thanks for the help, this all just seems a little weird to me. I didnt know that you could just essentially "foil" it like that
 
Last step
CXD = 2(AB)*BXA, because AXB = BXB = 0
 
thanks, you're a lifesaver! i totally get it now
 

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