How to determine what vector A is equal to?

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Homework Help Overview

The problem involves three vectors A, B, and C, defined by the equations A+B = 2C and B-2A = -C, with C given as a specific vector. The original poster seeks clarification on how to determine the value of vector A based on these relationships.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss how to manipulate the equations to isolate vector A, considering numerical approaches as a potential analogy. There is an exploration of combining equations and eliminating variables.

Discussion Status

The discussion is active, with participants engaging in exploring methods to combine the equations effectively. Some guidance has been offered regarding the elimination of variable B, indicating a productive direction in the conversation.

Contextual Notes

There is a mention of the challenge posed by the template's requirement for relevant equations, which some participants find awkward. The original poster's understanding of the unit vectors is noted, but it is recognized that this does not directly aid in solving the equations.

engphys204
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Homework Statement


Three vectors are related as by the equations: A+B = 2C and B-2A = -C.
If C= 1i + 2j +3k then what is vector A equal to?

Homework Equations


i, j, and k are unit vectors

The Attempt at a Solution


The solution in my answer key says that vector A = vector C but I don't understand how they arrived at that. Any clarification would be appreciated, thanks!
 
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Hi eng, :welcome:

A bit awkward if the template asks for relevant eqations, right ? You still need something there. The statement that ##\hat\imath, \hat \jmath, \hat k## are unit vectors is nice to form an idea, but it doesn't help solve the equations...

If A, B and C were numbers, how would you solve A+B = 2C & B-2A = -C ?
 
BvU said:
Hi eng, :welcome:

A bit awkward if the template asks for relevant eqations, right ? You still need something there. The statement that ##\hat\imath, \hat \jmath, \hat k## are unit vectors is nice to form an idea, but it doesn't help solve the equations...

If A, B and C were numbers, how would you solve A+B = 2C & B-2A = -C ?

Hi! Thanks for taking a look at my question and if they were numbers would I combine the 2 equations? A's and B's on one side with C's on the other and get A-2A + B+B = 2C-C (simplified: -A +2B = C)?
 
engphys204 said:
Hi! Thanks for taking a look at my question and if they were numbers would I combine the 2 equations? A's and B's on one side with C's on the other and get A-2A + B+B = 2C-C (simplified: -A +2B = C)?
You are looking for a relationship between A and C. So you need to combine the equations in a way which ... does what?
 
haruspex said:
You are looking for a relationship between A and C. So you need to combine the equations in a way which ... does what?
something that eliminates the B from the equation? Subtract them?
 
engphys204 said:
something that eliminates the B from the equation? Subtract them?
Of course.
 
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haruspex said:
Of course.
ohhh thanks I got it!
 

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