How to determine what vector A is equal to?

[engphys204]

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!

 

[BvU]

Hi eng,

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 ?

 

[engphys204]

Hi eng,

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)?

 

[haruspex]

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?

 

[engphys204]

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?

 

[haruspex]

something that eliminates the B from the equation? Subtract them?

Of course.

 

[engphys204]

Of course.

ohhh thanks I got it!