How to determine what vector A is equal to?

1. Apr 30, 2016

engphys204

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
i, j, and k are unit vectors

3. 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!

2. Apr 30, 2016

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 ?

3. Apr 30, 2016

engphys204

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)?

4. Apr 30, 2016

haruspex

You are looking for a relationship between A and C. So you need to combine the equations in a way which .... does what?

5. Apr 30, 2016

engphys204

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

6. Apr 30, 2016

haruspex

Of course.

7. Apr 30, 2016

engphys204

ohhh thanks I got it!