Vectors with uknowns problem

1. Jun 4, 2009

nickh89

1. The problem statement, all variables and given/known data
If A= (5.00 -7.00 ) units, B= (-7.00 + 2.00 ) units, and C= (27.0 + 20.0 ) units, determine a and b such that aA+ bB + C = 0.

2. Relevant equations
What I did to try and figure this out was solve for a and got the result of
a = -bB - C/ A

3. The attempt at a solution

What I did to try and solve this equation was plug that in for a, and take all the magnitudes of the vectors that are stated above but when i proceeded to do that everything would just cancel out when attempting to solve for b at that point. Any help would be great thank you.

2. Jun 4, 2009

Cyosis

You can't divide vectors like that. Secondly i take it that A=(5.00 , -7.00) is what you meant right? The way you have written it now suggests A=-2.

Plugging the components of the vectors into the vector equation will give you two "normal" equations. Since you have two unknowns and two equations you can solve a and b.

\begin{align} &5a-7b+27=0 \\ &-7a+2b+20=0 \end{align}

3. Jun 4, 2009

nickh89

yes it was A = (5i, -7j), and thank you very much for the help.