Solving the Triple Scalar Product: Finding the Value of a(dot)(a(cross)b)

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Homework Help Overview

The discussion revolves around the evaluation of the expression a·(a×b), where a and b are vectors. Participants are exploring the implications of the scalar and cross products in vector algebra.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the properties of the cross product and its relationship to the dot product, particularly focusing on the perpendicularity of the resulting vector. There are suggestions to explicitly calculate the cross product and then the dot product to uncover insights.

Discussion Status

The conversation is ongoing, with participants sharing thoughts on the nature of the problem and hinting at a "trick" involved in the calculation. There is no explicit consensus yet, but guidance has been offered regarding the approach to take.

Contextual Notes

One participant mentions the challenge of deriving a single value from the expression, indicating potential confusion about the underlying concepts. There is also a reference to the difficulty of the task, suggesting it may be part of a homework assignment with specific expectations.

CaityAnn
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Homework Statement


What is the value of a(dot)(a(cross)b) ? Why?
I am supposed to find an actual value.
Sorry I don't know code, these variables are all vectors. A is dotted with vectors a and b which are cross product.

Homework Equations


I know this can be written as a determinate of all three variables but I do not see how this gives me a single answer.


The Attempt at a Solution

 
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axb is perpendicular to a and b. The relevant part of this is that it is perpendicular to a, so axb is some vector c perpendicular to a. So what is a.c when c is perpendicular to a?
 
Try this, write out the cross product by hand.

Once you have the cross product, take the scalar product.

(There is a trick to this question, see if you can find it).
 
^ ^physicist, you're evil! Yes, once CaityAnn has gone through that pain, perhaps she will learn that it is better to think!
 
It may be evil, but I find if you work through it this way, after doing it a couple of times you start seeing the trick...
 

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