Constant vector and cross product?

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Homework Help Overview

The discussion revolves around evaluating the expression grad x (k x r), where r is defined as a vector in terms of its components and k is a constant vector. Participants are exploring the implications of the constant vector k and its representation.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the role of the constant vector k, with suggestions to assume an arbitrary form for k. Questions arise regarding the evaluation of the expression without knowing the specific components of k.

Discussion Status

There is an ongoing exploration of the problem, with participants sharing their results and questioning each other's reasoning. Some guidance has been offered regarding the assumption of k's form, and there is a recognition that the specific values of k may not be necessary for the evaluation.

Contextual Notes

Participants are discussing the implications of k being a constant vector and the assumptions that can be made in the absence of its specific components. There is a noted difference in the results obtained by different participants, highlighting the potential for multiple interpretations of the problem.

jlmac2001
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Okay, here's the question:

For r=xi + yj +zk evaluate grad x (k x r), where k is a constant vector.

I know how to do the cross product of k x r and I know how to do
grad x (k x r). But I don't know what k is. What's k?
 
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Originally posted by jlmac2001
... But I don't know what k is. What's k?
Try assuming an arbitrary k vector: ai + bj + ck (or whatever). Then see what happens.
 
does this look right?

The answer I got is: -2ai-2bj-2ck
 


Originally posted by jlmac2001
The answer I got is: -2ai-2bj-2ck
I got 2k (where k is the constant vector) but I did it quick. (So my answer differs by a minus sign from yours.) My main point was that you didn't have to know the value of k (the a, b, & c) to do the problem.
 
question

how did you just get 2k? i don't understand
 


Originally posted by jlmac2001
how did you just get 2k? i don't understand
By "2k" I mean: 2ai + 2bj + 2ck. (The same as you, but with a + instead of -.) [itex]2\vec{k}[/itex] is what I should have written. Make sense?
 
thanks

i get it now
 

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